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Journal articles on the topic 'Stochastic modelling theory'

Author: Grafiati

Published: 19 February 2023

Last updated: 20 February 2023

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1

Kołodziej, Joanna, William J. Knottenbelt, and Samee U. Khan. "Theory and Practice of Stochastic Modelling." Computers & Mathematics with Applications 64, no. 12 (December 2012): 3657. http://dx.doi.org/10.1016/j.camwa.2012.11.011.

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2

Fleishman, Benzion Semionovich. "Stochastic theory of community control." Ecological Modelling 39, no. 1-2 (November 1987): 121–59. http://dx.doi.org/10.1016/0304-3800(87)90017-2.

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3

Bertola, V., and E. Cafaro. "Deterministic–stochastic approach to compartment fire modelling." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2104 (December 9, 2008): 1029–41. http://dx.doi.org/10.1098/rspa.2008.0382.

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A generalized Semenov model is proposed to describe the dynamics of compartment fires. It is shown that the transitions to flashover or to extinction can be described in the context of the catastrophe theory (or the theory of dynamical systems) by introducing a suitable potential function of the smoke layer temperature. The effect on the fire dynamics of random perturbations is then studied by introducing a random noise term accounting for internal and external perturbations with an arbitrary degree of correlation. While purely Gaussian perturbations (white noise) do not change the behaviour of the fire with respect to the deterministic model, perturbations depending on the model variable (‘coloured’ noise) may drive the system to different states. This suggests that the compartment fires can be controlled or driven to extinction by introducing appropriate external perturbations.

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4

Frederiksen, Jorgen S., Terence J. O'Kane, and Meelis J. Zidikheri. "Subgrid modelling for geophysical flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1982 (January 13, 2013): 20120166. http://dx.doi.org/10.1098/rsta.2012.0166.

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Recently developed closure-based and stochastic model approaches to subgrid-scale modelling of eddy interactions are reviewed. It is shown how statistical dynamical closure models can be used to self-consistently calculate the eddy damping and stochastic backscatter parameters, required in large eddy simulations (LESs), from higher resolution simulations. A closely related direct stochastic modelling scheme that is more generally applicable to complex models is then described and applied to LESs of quasi-geostrophic turbulence of the atmosphere and oceans. The fundamental differences between atmospheric and oceanic LESs, which are related to the difference in the deformation scales in the two classes of flows, are discussed. It is noted that a stochastic approach may be crucial when baroclinic instability is inadequately resolved. Finally, inhomogeneous closure theory is applied to the complex problem of flow over topography; it is shown that it can be used to understand the successes and limitations of currently used heuristic schemes and to provide a basis for further developments in the future.

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5

Grum, Morten. "Incorporating concepts from physical theory into stochastic modelling of urban runoff pollution." Water Science and Technology 37, no. 1 (January 1, 1998): 179–85. http://dx.doi.org/10.2166/wst.1998.0044.

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On evaluating the present or future state of integrated urban water systems, sewer drainage models, with rainfall as primary input, are often used to calculate the expected return periods of given detrimental acute pollution events and the uncertainty thereof. The model studied in the present paper incorporates notions of physical theory in a stochastic model of water level and particulate chemical oxygen demand (COD) at the overflow point of a Dutch combined sewer system. A stochastic model based on physical mechanisms has been formulated in continuous time. The extended Kalman filter has been used in conjunction with a maximum likelihood criteria and a non-linear state space formulation to decompose the error term into system noise terms and measurement errors. The bias generally obtained in deterministic modelling, by invariably and often inappropriately assuming all error to result from measurement inaccuracies, is thus avoided. Continuous time stochastic modelling incorporating physical, chemical and biological theory presents a possible modelling alternative. These preliminary results suggest that further work is needed in order to fully appreciate the method's potential and limitations in the field of urban runoff pollution modelling.

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6

Špaček, Miroslav. "Business Process Risk Modelling in Theory and Practice." Quality Innovation Prosperity 25, no. 1 (March 31, 2021): 55–72. http://dx.doi.org/10.12776/qip.v25i1.1551.

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Purpose: The purpose of the paper is to introduce SW based decision-making tool that helps managers cope with risks and uncertainties of selected industrial processes. The solution is substantiated by the theoretical background. Methodology/Approach: The research is based on combination of contextual interviews with process management experts and Business Process Modelling Notion (BPMN). The former is aimed at the identification of industrial processes with highest risk exposure the latter is conducive to the design of processes to be subjected to stochastic simulation. Findings: The findings show that the risks and uncertainties in the management of industrial processes can be kept under control when using advanced tools of risk analysis as simulation approaches. The solution proposed comes in handy to risk analysts or process managers. Research Limitation/Implication: The library of process models which were included into stochastic simulation includes selected processes as investments, service providing or economic value-added engineering. Additional processes are being included on ongoing basis. Originality/Value of paper: The paper offers the solution to industrial process risk management which goes far beyond academic sphere and provides industrial practitioners SW tool that facilitates process risk management.

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7

Amirdjanova, Anna. "Vortex theory approach to stochastic hydrodynamics." Mathematical and Computer Modelling 45, no. 11-12 (June 2007): 1319–41. http://dx.doi.org/10.1016/j.mcm.2006.11.001.

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8

Anastassiou, George A. "Multivariate stochastic Korovkin theory given quantitatively." Mathematical and Computer Modelling 48, no. 3-4 (August 2008): 558–80. http://dx.doi.org/10.1016/j.mcm.2007.04.022.

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9

Gulbinovič, Lech. "TECHNIQUES FOR MODELLING NETWORK SECURITY / KOMPIUTERIŲ SISTEMŲ SAUGUMO MODELIAVIMAS." Mokslas - Lietuvos ateitis 4, no. 1 (April 23, 2012): 27–30. http://dx.doi.org/10.3846/mla.2012.06.

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The article compares modelling techniques for network security, including the theory of probability, Markov processes, Petri networks and application of stochastic activity networks. The paper introduces the advantages and disadvantages of the above proposed methods and accepts the method of modelling the network of stochastic activity as one of the most relevant. The stochastic activity network allows modelling the behaviour of the dynamic system where the theory of probability is inappropriate. A real network distributes incidents referring to various distribution methods (exponential, gama, Veibul, etc.). A real system should evaluate time value when the stochastic activity network allows such activity. Santrauka Nagrinėjami šiuo metu žinomi kompiuterių sistemų saugumo modeliavimo metodai: tikimybių teorijos, Markovo procesų, Petri tinklų ir stochastinių veiklos tinklų. Šie metodai leidžia modeliuoti dinamines sistemas, kurioms kombinatoriniai metodai yra netinkami. Kadangi kompiuterių tinkluose įvykiai gali būti pasiskirstę ne tik pagal eksponentinį dėsnį, todėl jiems modeliuoti netinka Markovo procesų ir Petri tinklų modeliai. Realiuose tinkluose įvykiai gali būti pasiskirstę pagal eksponentinį, gama, Veibulo ir kt. dėsnius. Parodyta, kad iš aptartų šiuo metu žinomų modeliavimo metodų pagrindiniams saugumo veiksniams įvertinti tinkamiausias yra stochastinės veiklos tinklų metodas.

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10

Milz, Simon, Fattah Sakuldee, Felix A. Pollock, and Kavan Modi. "Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories." Quantum 4 (April 20, 2020): 255. http://dx.doi.org/10.22331/q-2020-04-20-255.

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In classical physics, the Kolmogorov extension theorem lays the foundation for the theory of stochastic processes. It has been known for a long time that, in its original form, this theorem does not hold in quantum mechanics. More generally, it does not hold in any theory of stochastic processes -- classical, quantum or beyond -- that does not just describe passive observations, but allows for active interventions. Such processes form the basis of the study of causal modelling across the sciences, including in the quantum domain. To date, these frameworks have lacked a conceptual underpinning similar to that provided by Kolmogorov’s theorem for classical stochastic processes. We prove a generalized extension theorem that applies to all theories of stochastic processes, putting them on equally firm mathematical ground as their classical counterpart. Additionally, we show that quantum causal modelling and quantum stochastic processes are equivalent. This provides the correct framework for the description of experiments involving continuous control, which play a crucial role in the development of quantum technologies. Furthermore, we show that the original extension theorem follows from the generalized one in the correct limit, and elucidate how a comprehensive understanding of general stochastic processes allows one to unambiguously define the distinction between those that are classical and those that are quantum.

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11

Birnir, B., J. Hernandez, and T. R. Smith. "The Stochastic Theory of Fluvial Landsurfaces." Journal of Nonlinear Science 17, no. 1 (October 17, 2006): 13–57. http://dx.doi.org/10.1007/s00332-005-0688-3.

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12

Gradoni, Gabriele, Johannes Russer, Mohd Hafiz Baharuddin, Michael Haider, Peter Russer, Christopher Smartt, Stephen C. Creagh, Gregor Tanner, and David W. P. Thomas. "Stochastic electromagnetic field propagation— measurement and modelling." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2134 (October 29, 2018): 20170455. http://dx.doi.org/10.1098/rsta.2017.0455.

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This paper reviews recent progress in the measurement and modelling of stochastic electromagnetic fields, focusing on propagation approaches based on Wigner functions and the method of moments technique. The respective propagation methods are exemplified by application to measurements of electromagnetic emissions from a stirred, cavity-backed aperture. We discuss early elements of statistical electromagnetics in Heaviside's papers, driven mainly by an analogy of electromagnetic wave propagation with heat transfer. These ideas include concepts of momentum and directionality in the realm of propagation through confined media with irregular boundaries. We then review and extend concepts using Wigner functions to propagate the statistical properties of electromagnetic fields. We discuss in particular how to include polarization in this formalism leading to a Wigner tensor formulation and a relation to an averaged Poynting vector. This article is part of the theme issue ‘Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’’.

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13

Cuchiero, Christa. "Polynomial processes in stochastic portfolio theory." Stochastic Processes and their Applications 129, no. 5 (May 2019): 1829–72. http://dx.doi.org/10.1016/j.spa.2018.06.007.

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14

Brethé, Jean-François, Eric Vasselin, Dimitri Lefebvre, and Brayima Dakyo. "Modelling of repeatability phenomena using the stochastic ellipsoid approach." Robotica 24, no. 4 (December 6, 2005): 477–90. http://dx.doi.org/10.1017/s0263574705002481.

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A stochastic ellipsoid modelling of repeatability is proposed for industrial manipulator robots. The covariance matrix of angular position is determined introducing the jump process, which reveals to be a first and second order stationary Gaussian process.From this accurate covariance matrix, the stochastic ellipsoid theory gives the density of position in the workspace around the mean position. Hence the pose repeatability index can be computed in different locations. Computed and experimental repeatability are compared. Experimental repeatability variability is studied. A new “intrinsic repeatability index” is proposed. In conclusion, the modelling reflects well the location and load influence on the repeatability.

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15

Kitaura, Francisco-Shu, Gustavo Yepes, and Francisco Prada. "Modelling baryon acoustic oscillations with perturbation theory and stochastic halo biasing." Monthly Notices of the Royal Astronomical Society: Letters 439, no. 1 (December 31, 2013): L21—L25. http://dx.doi.org/10.1093/mnrasl/slt172.

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16

Kong, Weili, and Yuanfu Shao. "Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction." Discrete Dynamics in Nature and Society 2020 (February 10, 2020): 1–19. http://dx.doi.org/10.1155/2020/1053401.

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Considering periodic environmental changes and random disturbance, we explore the dynamical behaviors of a stochastic competitive system with impulsive and periodic parameters in this paper. Firstly, by use of extreme-value theory of quadratic function and constructing suitable functional, we study the existence of periodic Markovian process. Secondly, by comparison theory of the stochastic differential equation, we study the extinction and permanence in the mean of all species. Thirdly, applying an important lemma, we investigate the stochastic persistence of this system. Finally, some numerical simulations are given to illustrate the main results.

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17

HÜFFEL, HELMUTH. "NONLINEAR PHENOMENA IN CANONICAL STOCHASTIC QUANTIZATION." International Journal of Bifurcation and Chaos 18, no. 09 (September 2008): 2787–91. http://dx.doi.org/10.1142/s0218127408022019.

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Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochastic process. We discuss a novel formulation of the Higgs mechanism in QED.

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18

Acosta-Humánez, Primitivo B., José A. Capitán, and Juan J. Morales-Ruiz. "Integrability of stochastic birth-death processes via differential Galois theory." Mathematical Modelling of Natural Phenomena 15 (2020): 70. http://dx.doi.org/10.1051/mmnp/2020005.

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Stochastic birth-death processes are described as continuous-time Markov processes in models of population dynamics. A system of infinite, coupled ordinary differential equations (the so-called master equation) describes the time-dependence of the probability of each system state. Using a generating function, the master equation can be transformed into a partial differential equation. In this contribution we analyze the integrability of two types of stochastic birth-death processes (with polynomial birth and death rates) using standard differential Galois theory. We discuss the integrability of the PDE via a Laplace transform acting over the temporal variable. We show that the PDE is not integrable except for the case in which rates are linear functions of the number of individuals.

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19

Canevet, C., S. Gilmore, J. Hillston, M. Prowse, and P. Stevens. "Performance modelling with the unified modelling language and stochastic process algebras." IEE Proceedings - Computers and Digital Techniques 150, no. 2 (2003): 107. http://dx.doi.org/10.1049/ip-cdt:20030084.

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20

Norman, G. E., and V. V. Stegailov. "Stochastic theory of the classical molecular dynamics method." Mathematical Models and Computer Simulations 5, no. 4 (July 2013): 305–33. http://dx.doi.org/10.1134/s2070048213040108.

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21

Zhang, Yi, Na Li, and Jianyu Zhang. "Stochastic stability and Hopf bifurcation analysis of a singular bio-economic model with stochastic fluctuations." International Journal of Biomathematics 12, no. 08 (November 2019): 1950083. http://dx.doi.org/10.1142/s1793524519500839.

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In this paper, we study a class of singular stochastic bio-economic models described by differential-algebraic equations due to the influence of economic factors. Simplifying the model through a stochastic averaging method, we obtained a two-dimensional diffusion process of averaged amplitude and phase. Stochastic stability and Hopf bifurcations can be analytically determined based on the singular boundary theory of diffusion process, the Maximal Lyapunov exponent and the invariant measure theory. The critical value of the stochastic Hopf bifurcation parameter is obtained and the position of Hopf bifurcation drifting with the parameter increase is presented as a result. Practical example is presented to verify the effectiveness of the results.

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22

Carta, Alessandro, and Mark F. J. Steel. "Modelling multi-output stochastic frontiers using copulas." Computational Statistics & Data Analysis 56, no. 11 (November 2012): 3757–73. http://dx.doi.org/10.1016/j.csda.2010.07.007.

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23

Brockwell, Peter J. "Stochastic models in cell kinetics." Journal of Applied Probability 25, A (1988): 91–111. http://dx.doi.org/10.2307/3214149.

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We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

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24

Brockwell, Peter J. "Stochastic models in cell kinetics." Journal of Applied Probability 25, A (1988): 91–111. http://dx.doi.org/10.1017/s0021900200040286.

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We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

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25

Xia, Pengcheng, Longjie Xie, Xicheng Zhang, and Guohuan Zhao. "Lq(Lp)-theory of stochastic differential equations." Stochastic Processes and their Applications 130, no. 8 (August 2020): 5188–211. http://dx.doi.org/10.1016/j.spa.2020.03.004.

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26

Al-Hussein, A., and K. D. Elworthy. "Infinite-dimensional degree theory and stochastic analysis." Journal of Fixed Point Theory and Applications 7, no. 1 (May 13, 2010): 33–65. http://dx.doi.org/10.1007/s11784-010-0009-9.

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27

Rihan, Fathalla A., Chinnathambi Rajivganthi, and Palanisamy Muthukumar. "Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control." Discrete Dynamics in Nature and Society 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/5394528.

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In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. Finally, we provide an example to illustrate the obtained results.

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28

Korman, Can E., and Isaak D. Mayergoyz. "On hysteresis of ion channels." Mathematical Modelling of Natural Phenomena 15 (2020): 26. http://dx.doi.org/10.1051/mmnp/2019058.

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Ion channel proteins have many conformational (metastable) states and, for this reason, they exhibit hysteresis. This fact is responsible for the non-Markovian stochastic nature of single ion channel recordings. It is suggested in the paper that the stochastic single channel recordings can be modeled as the random outputs of rectangular hysteresis loops driven by stochastic processes. The latter problem can be mathematically treated as an exit problem for stochastic processes or by using the theory of stochastic processes on graphs. It is also demonstrated in the paper that the collective action of sodium and potassium channels responsible for the generation and propagation of action potentials exhibit hysteresis. This demonstration is accomplished by using the inverse problem approach to the nonlinear Hodgkin-Huxley diffusion equation.

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29

GASBARRA, DARIO, JOSÉ IGOR MORLANES, and ESKO VALKEILA. "INITIAL ENLARGEMENT IN A MARKOV CHAIN MARKET MODEL." Stochastics and Dynamics 11, no. 02n03 (September 2011): 389–413. http://dx.doi.org/10.1142/s021949371100336x.

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Enlargement of filtrations is a classical topic in the general theory of stochastic processes. This theory has been applied to stochastic finance in order to analyze models with insider information. In this paper we study initial enlargement in a Markov chain market model, introduced by Norberg. In the enlarged filtration, several things can happen: some of the jumps times can be accessible or predictable, but in the original filtration all the jumps times are totally inaccessible. But even if the jumps times change to accessible or predictable, the insider does not necessarily have arbitrage possibilities.

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30

TEICHMANN, JOSEF. "ANOTHER APPROACH TO SOME ROUGH AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 11, no. 02n03 (September 2011): 535–50. http://dx.doi.org/10.1142/s0219493711003437.

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In this paper, we introduce a new approach to rough and stochastic partial differential equations (RPDEs and SPDEs): we consider general Banach spaces as state spaces and — for the sake of simplicity — finite dimensional sources of noise, either rough or stochastic. By means of a time-dependent transformation of state space and rough path theory, we are able to construct unique solutions of the respective R- and SPDEs. As a consequence of our construction, we can apply the pool of results of rough path theory, in particular we can obtain strong and weak numerical schemes of high order converging to the solution process.

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31

Scarpa, Luca, and Ulisse Stefanelli. "Doubly nonlinear stochastic evolution equations." Mathematical Models and Methods in Applied Sciences 30, no. 05 (May 2020): 991–1031. http://dx.doi.org/10.1142/s0218202520500219.

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Nonlinear diffusion problems featuring stochastic effects may be described by stochastic partial differential equations of the form [Formula: see text] We present an existence theory for such equations under general monotonicity assumptions on the nonlinearities. In particular, [Formula: see text], [Formula: see text], and [Formula: see text] are allowed to be multivalued, as required by the modelization of solid–liquid phase transitions. In this regard, the equation corresponds to a nonlinear-diffusion version of the classical two-phase Stefan problem with stochastic perturbation. The existence of martingale solutions is proved via regularization and passage-to-the-limit. The identification of the limit is obtained by a lower-semicontinuity argument based on a suitably generalized Itô’s formula. Under some more restrictive assumptions on the nonlinearities, existence and uniqueness of strong solutions follows. Besides the relation above, the theory covers equations with nonlocal terms as well as systems.

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32

Li, Yajie, and Xinzhu Meng. "Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment." Discrete Dynamics in Nature and Society 2019 (February 24, 2019): 1–15. http://dx.doi.org/10.1155/2019/5498569.

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This paper proposes a novel impulsive stochastic nonautonomous chemostat model with the saturated and bilinear growth rates in a polluted environment. Using the theory of impulsive differential equations and Lyapunov functions method, we first investigate the dynamics of the stochastic system and establish the sufficient conditions for the extinction and the permanence of the microorganisms. Then we demonstrate that the stochastic periodic system has at least one nontrivial positive periodic solution. The results show that both impulsive toxicant input and stochastic noise have great effects on the survival and extinction of the microorganisms. Furthermore, a series of numerical simulations are presented to illustrate the performance of the theoretical results.

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33

CARMONA, S. C., and M. I. FREIDLIN. "ON LOGARITHMIC ASYMPTOTICS OF STOCHASTIC RESONANCE FREQUENCIES." Stochastics and Dynamics 03, no. 01 (March 2003): 55–71. http://dx.doi.org/10.1142/s0219493703000607.

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Stochastic resonance effects due to arbitrarily small amplitude deterministic perturbations in dynamical systems with noise are studied. The concept of Log-Asymptotic Resonance Frequency is introduced and the relationship between its existence and some types of symmetries in the stochastic system is established; the spectrum of this kind of frequencies is determined. These symmetries are defined through the quasi-deterministic approximation of the system. The large deviation theory gives the basic machinery for this analysis.

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34

Kolářová, Edita. "Applications of second order stochastic integral equations to electrical networks." Tatra Mountains Mathematical Publications 63, no. 1 (June 1, 2015): 163–73. http://dx.doi.org/10.1515/tmmp-2015-0028.

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The theory of stochastic differential equations is used in various fields of science and engineering. This paper deals with vector-valued stochastic integral equations. We show some applications of the presented theory to the problem of modelling RLC electrical circuits by noisy parameters. From practical point of view, the second-order RLC circuits are of major importance, as they are the building blocks of more complex physical systems. The mathematical models of such circuits lead to the second order differential equations. We construct stochastic models of the RLC circuit by replacing a coefficient in the deterministic system with a noisy one. In this paper we present the analytic solution of these equations using the Itô calculus and compute confidence intervals for the stochastic solutions. Numerical simulations in the examples are performed using Matlab.

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35

Hong, Desheng, Zuoliang Xiong, and Cuiping Yang. "Analysis of Adaptive Synchronization for Stochastic Neutral-Type Memristive Neural Networks with Mixed Time-Varying Delays." Discrete Dynamics in Nature and Society 2018 (2018): 1–13. http://dx.doi.org/10.1155/2018/8126127.

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Linear feedback control and adaptive feedback control are proposed to achieve the synchronization of stochastic neutral-type memristive neural networks with mixed time-varying delays. By applying the stochastic differential inclusions theory, Lyapunov functional, and linear matrix inequalities method, we obtain some new adaptive synchronization criteria. A numerical example is given to illustrate the effectiveness of our results.

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36

Kurkina, M. V., and V. V. Slavsky. "Stochastic Modelling of Closed Curves in the Plane." Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 14, no. 1 (2021): 39–49. http://dx.doi.org/10.14529/mmp210103.

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37

Núñez-López, Mayra, Eymard Hernández-López, and Joaquín Delgado. "Stochastic Simulation on a Minimal Model of Cancer Immunoediting Theory." International Journal of Bifurcation and Chaos 31, no. 06 (May 2021): 2150088. http://dx.doi.org/10.1142/s0218127421500887.

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In this paper, we explore the interplay between tumor cells and the human immune system, based on a deterministic mathematical model of minimal interactions by transforming it to stochastic model using a continuous-time Markov chain, where time is continuous but the state space is discrete. Furthermore, we simulate the stochastic basin of attraction to verify the behavior of the three critical points of interest in the deterministic system. Moreover, the stochastic simulations exemplify the cancer immunoediting theory in its three phases of development: elimination, equilibrium and escape. We extend the minimum model proposed in [DeLisi & Rescigno, 1977] to include a term of immunotherapy by lymphocyte injection, and we simulate two treatment regimes, equilibrium and escape, under several schemes.

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38

Gellner, Gabriel, Kevin S. McCann, and Alan Hastings. "The duality of stability: towards a stochastic theory of species interactions." Theoretical Ecology 9, no. 4 (May 27, 2016): 477–85. http://dx.doi.org/10.1007/s12080-016-0303-2.

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39

Kuhwald, Isabelle, and Ilya Pavlyukevich. "Stochastic resonance with multiplicative heavy-tailed Lévy noise: Optimal tuning on an algebraic time scale." Stochastics and Dynamics 17, no. 04 (May 4, 2017): 1750027. http://dx.doi.org/10.1142/s0219493717500277.

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Stochastic resonance is an amplification and synchronization effect of weak periodic signals in nonlinear systems through a small noise perturbation. In this paper we study the dynamics of stochastic resonance in a bistable system driven by multiplicative Lévy noise with heavy tails, e.g., [Formula: see text]-stable Lévy noise. We determine the optimal tuning with respect to a probabilistic synchronization measure for both the jump-diffusion and the reduced two-state Markov chain. These results extend the theory of stochastic resonance to the case of heavy tail Lévy perturbations.

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40

Abdelghani, Mohamed, and Alexander Melnikov. "A comparison theorem for stochastic equations of optional semimartingales." Stochastics and Dynamics 18, no. 04 (August 2018): 1850029. http://dx.doi.org/10.1142/s0219493718500296.

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This paper is devoted to comparison of strong solutions of stochastic equations with respect to optional semimartingales. Optional semimartingales have right and left limits but are not necessarily continuous and therefore defined on “unusual” probability spaces. Integration theory with respect to optional semimartingales is well-developed. However, not much attention is given to stochastic integral equations of optional semimartingales. A pathwise comparison result for strong solutions of a very general class of optional stochastic equations with non-lipshitz coefficients is given. Moreover, simple applications to mathematical finance is presented.

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41

Palanichamy, Jegathambal, Torsten Becker, Martin Spiller, Jürgen Köngeter, and Sankaralingam Mohan. "Multicomponent reaction modelling using a stochastic algorithm." Computing and Visualization in Science 12, no. 2 (October 20, 2007): 51–61. http://dx.doi.org/10.1007/s00791-007-0080-y.

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BERTOTTI, MARIA LETIZIA, and MARCELLO DELITALA. "FROM DISCRETE KINETIC AND STOCHASTIC GAME THEORY TO MODELLING COMPLEX SYSTEMS IN APPLIED SCIENCES." Mathematical Models and Methods in Applied Sciences 14, no. 07 (July 2004): 1061–84. http://dx.doi.org/10.1142/s0218202504003544.

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This paper deals with some methodological aspects related to the discretization of a class of integro-differential equations modelling the evolution of the probability distribution over the microscopic state of a large system of interacting individuals. The microscopic state includes both mechanical and socio-biological variables. The discretization of the microscopic state generates a class of dynamical systems defining the evolution of the densities of the discretized state. In general, this yields a system of partial differential equations replacing the continuous integro-differential equation. As an example, a specific application is discussed, which refers to modelling in the field of social dynamics. The derivation of the evolution equation needs the development of a stochastic game theory.

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Kim, Jeong-Hoon. "Asymptotic theory of noncentered mixing stochastic differential equations." Stochastic Processes and their Applications 114, no. 1 (November 2004): 161–74. http://dx.doi.org/10.1016/j.spa.2004.05.004.

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Loutsenko, Igor, and Oksana Yermolayeva. "On integrability and exact solvability in deterministic and stochastic Laplacian growth." Mathematical Modelling of Natural Phenomena 15 (2020): 3. http://dx.doi.org/10.1051/mmnp/2019033.

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We review applications of theory of classical and quantum integrable systems to the free-boundary problems of fluid mechanics as well as to corresponding problems of statistical mechanics. We also review important exact results obtained in the theory of multi-fractal spectra of the stochastic models related to the Laplacian growth: Schramm-Loewner and Levy-Loewner evolutions.

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BELOPOLSKAYA, YANA, and WOJBOR A. WOYCZYNSKI. "GENERALIZED SOLUTIONS OF THE CAUCHY PROBLEM FOR SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS AND DIFFUSION PROCESSES." Stochastics and Dynamics 12, no. 01 (March 2012): 1150001. http://dx.doi.org/10.1142/s0219493712003523.

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The purpose of this paper is to construct both strong and weak solutions (in certain functional classes) of the Cauchy problem for a class of systems of nonlinear parabolic equations via a unified stochastic approach. To this end we give a stochastic interpretation of such a system, treating it as a version of the backward Kolmogorov equation for a two-component Markov process with coefficients depending on the distribution of its first component. To extend this approach and apply it to the construction of a generalized solution of a system of nonlinear parabolic equations, we use results from Kunita's theory of stochastic flows.

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Schimansky-Geier, Lutz, Jan A. Freund, Alexander B. Neiman, and Boris Shulgin. "Noise Induced Order: Stochastic Resonance." International Journal of Bifurcation and Chaos 08, no. 05 (May 1998): 869–79. http://dx.doi.org/10.1142/s021812749800067x.

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We investigate stochastic resonance in the framework of information theory. Input signals are taken from an electronic circuit and output signals are produced by a Schmitt trigger. These electronic signals are analyzed with respect to their informational contents. Conditional entropies and Kullback measures exhibit extrema for values of noise intensity in the range of stochastic resonance. However, it has to be noted that these extrema are related to synchronization effects, observed in stochastic resonance for large signal amplitudes, rather than to a peak in the related spectrum indicating some periodic component.

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Zhou, Chuang, XinJiang Lu, and MingHui Huang. "Dempster–Shafer theory-based robust least squares support vector machine for stochastic modelling." Neurocomputing 182 (March 2016): 145–53. http://dx.doi.org/10.1016/j.neucom.2015.11.081.

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Kim, Sangdan, Suhee Han, and Eungseock Kim. "Stochastic modelling of soil water and plant water stress using cumulant expansion theory." Ecohydrology 4, no. 1 (January 2011): 94–105. http://dx.doi.org/10.1002/eco.127.

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Song, Mingzhu, Quanxin Zhu, and Hongwei Zhou. "Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms." Discrete Dynamics in Nature and Society 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/2487957.

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The stability issue is investigated for a class of stochastic neural networks with time delays in the leakage terms. Different from the previous literature, we are concerned with the almost sure stability. By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s formula, and stochastic analysis theory, some novel sufficient conditions are derived to guarantee the almost sure stability of the equilibrium point. In particular, the weak infinitesimal operator of Lyapunov functions in this paper is not required to be negative, which is necessary in the study of the traditional moment stability. Finally, two numerical examples and their simulations are provided to show the effectiveness of the theoretical results and demonstrate that time delays in the leakage terms do contribute to the stability of stochastic neural networks.

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Barnsley, Michael F., Anca Deliu, and Ruifeng Xie. "Stationary Stochastic Processes and Fractal Data Compression." International Journal of Bifurcation and Chaos 07, no. 03 (March 1997): 551–67. http://dx.doi.org/10.1142/s021812749700039x.

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It is shown that the invariant measure of a stationary nonatomic stochastic process yields an iterated function system with probabilities and an associated dynamical system that provide the basis for optimal lossless data compression algorithms. The theory is illustrated for the case of finite-order Markov processes: For a zero-order process, it produces the arithmetic compression method; while for higher order processes it yields dynamical systems, constructed from piecewise affine mappings from the interval [0, 1] into itself, that may be used to store information efficiently. The theory leads to a new geometrical approach to the development of compression algorithms.

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