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Journal articles on the topic 'Stochastic processes Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 January 2023

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1

Veretennikov, Alexander. "Stochastic Processes and Models." Bulletin of the London Mathematical Society 39, no. 1 (January 16, 2007): 167–69. http://dx.doi.org/10.1112/blms/bdl020.

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2

Jaeger, Herbert. "Observable Operator Models for Discrete Stochastic Time Series." Neural Computation 12, no. 6 (June 1, 2000): 1371–98. http://dx.doi.org/10.1162/089976600300015411.

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A widely used class of models for stochastic systems is hidden Markov models. Systems that can be modeled by hidden Markov models are a proper subclass of linearly dependent processes, a class of stochastic systems known from mathematical investigations carried out over the past four decades. This article provides a novel, simple characterization of linearly dependent processes, called observable operator models. The mathematical properties of observable operator models lead to a constructive learning algorithm for the identification of linearly dependent processes. The core of the algorithm h

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3

Nikolova, Iveta. "On stochastic models in biology and medicine." Asian-European Journal of Mathematics 13, no. 08 (May 21, 2020): 2050168. http://dx.doi.org/10.1142/s1793557120501685.

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Stochastic models along with deterministic models are successfully used for mathematical description of biological processes. They apply knowledge from probability theory and mathematical statistics to analyze specific characteristics of living systems. The paper is devoted to some stochastic models of various phenomena in biology and medicine. Basic concepts and definitions used in classical probability models are considered and illustrated by several examples with solutions. The stochastic kinetic modeling approach is described. A new kinetic model of autoimmune disease is presented. It is a

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4

Butov, Alexander A., Maxim A. Volkov, Viktor N. Golovanov, Anatoly A. Kovalenko, Boris M. Kostishko, and Leonid M. Samoilov. "Mathematical Modeling of Main Classes of Stochastic Productive Systems." Engineering Technologies and Systems 29, no. 4 (December 31, 2019): 496–509. http://dx.doi.org/10.15507/2658-4123.029.201904.496-509.

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Introduction. The article deals with mathematical models of two main classes of processes in stochastic productive systems. For a multistage system, conditions of belonging to a “just-in-time” class or a class with infinite support of the time distribution function for productive operations are determined. Materials and Methods. Descriptions and investigations of models are carried out by trajectory (martingale) methods. For “just-in-time” systems and multistage stochastic productive systems, terms and methods of random walks in a random environment and birth and death processes are used. The

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5

Larina, Ludmila, Dmitryi Ruslyakov, Olga Tikhonova, and Boris Kalmykov. "Research of processes of the heatmass transfer in the porous environments having stochastic characteristics on the basis of methods of applied synergetic." E3S Web of Conferences 273 (2021): 01023. http://dx.doi.org/10.1051/e3sconf/202127301023.

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On the basis of a synergetic approach, mathematical models of the stochastic similarity of the functioning of heat and mass transfer processes in porous media (grain materials) have been developed. In these models, the indicators of the stochastic characteristics of these media are combined with the parameters of the processes of hygrothermal treatment under vacuum conditions: residual pressure - P, temperature - T, time-τ, with a density of couple - ρ. The resulting models can be used to control hygrothermal processes in the processing of natural tanning and grain materials that have a stocha

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6

Rota, Gian-Carlo. "Stochastic models for social processes." Advances in Mathematics 57, no. 1 (July 1985): 91. http://dx.doi.org/10.1016/0001-8708(85)90110-0.

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7

Belopolskaya, Ya I. "Stochastic Models of Chemotaxis Processes." Journal of Mathematical Sciences 251, no. 1 (October 12, 2020): 1–14. http://dx.doi.org/10.1007/s10958-020-05059-7.

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8

Holubec, Viktor, Artem Ryabov, Sarah A. M. Loos, and Klaus Kroy. "Equilibrium stochastic delay processes." New Journal of Physics 24, no. 2 (February 1, 2022): 023021. http://dx.doi.org/10.1088/1367-2630/ac4b91.

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Abstract Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is available for linear models only. We introduce a class of stochastic delay processes with nonlinear time-local forces and linear time-delayed forces that obey fluctuation theorems and converge to a Boltzmann equilibrium at long times. From the point of view of control theory, such ‘equilibrium stochastic delay processes’ are stable and energetically

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9

Anh, V. V., C. C. Heyde, and Q. Tieng. "Stochastic models for fractal processes." Journal of Statistical Planning and Inference 80, no. 1-2 (August 1999): 123–35. http://dx.doi.org/10.1016/s0378-3758(98)00246-8.

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10

Butusov, O. B., O. P. Nikiforova, and N. I. Redikultseva. "Mathematical methods for the analysis of migration processes on the basis of demographic data." Izvestiya MGTU MAMI 9, no. 1-4 (July 10, 2015): 21–25. http://dx.doi.org/10.17816/2074-0530-67102.

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The problem of mathematical analysis of demographic data was investigated for data, where information on migration flows is taken into account implicitly. Regression techniques, neural networks and stochastic analysis were used for the mathematical analysis of demographic processes. Two age groups were considered: young (0 - 39 years) and elderly (40 - 70 years). While development of stochastic models the theory of Markov chains and transition matrix were used. The parameterization and model identification were conducted according to Rosstat data.

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11

Wilks, Daniel S. "Effects of stochastic parametrization on conceptual climate models." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1875 (April 29, 2008): 2475–88. http://dx.doi.org/10.1098/rsta.2008.0005.

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Conceptual climate models are very simple mathematical representations of climate processes, which are especially useful because their workings can be readily understood. The usual procedure of representing effects of unresolved processes in such models using functions of the prognostic variables (parametrizations) that include no randomness generally results in these models exhibiting substantially less variability than do the phenomena they are intended to simulate. A viable yet still simple alternative is to replace the conventional deterministic parametrizations with stochastic parametriza

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12

Averina, Tatyana A., and Konstantin A. Rybakov. "Using maximum cross section method for filtering jump-diffusion random processes." Russian Journal of Numerical Analysis and Mathematical Modelling 35, no. 2 (April 28, 2020): 55–67. http://dx.doi.org/10.1515/rnam-2020-0005.

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Abstract The paper is focused on problem of filtering random processes in dynamical systems whose mathematical models are described by stochastic differential equations with a Poisson component. The solution of a filtering problem supposes simulation of trajectories of solutions to a stochastic differential equation. The trajectory modelling procedure includes simulation of a Poisson flow permitting application of the maximum cross section method and its modification.

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13

Щелкалін, Віталій Миколайович. "Mathematical models and methods for prediction and control of interrelated nonstationary stochastic processes." Technology audit and production reserves 6, no. 4(8) (December 13, 2012): 29–30. http://dx.doi.org/10.15587/2312-8372.2012.5643.

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14

MELNIK, RODERICK V. N., XILIN WEI, and GABRIEL MORENO–HAGELSIEB. "NONLINEAR DYNAMICS OF CELL CYCLES WITH STOCHASTIC MATHEMATICAL MODELS." Journal of Biological Systems 17, no. 03 (September 2009): 425–60. http://dx.doi.org/10.1142/s0218339009002879.

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Cell cycles are fundamental components of all living organisms and their systematic studies extend our knowledge about the interconnection between regulatory, metabolic, and signaling networks, and therefore open new opportunities for our ultimate efficient control of cellular processes for disease treatments, as well as for a wide variety of biomedical and biotechnological applications. In the study of cell cycles, nonlinear phenomena play a paramount role, in particular in those cases where the cellular dynamics is in the focus of attention. Quantification of this dynamics is a challenging t

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15

Safarova, Aygun, and Javida Damirova. "Research and modeling of oil refining technological processes operating in the condition of stochastic uncertainty." EUREKA: Physics and Engineering, no. 5 (September 30, 2022): 91–98. http://dx.doi.org/10.21303/2461-4262.2022.002523.

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As it is known, one of the initial and important stages in the creation of optimal control systems of oil refining technological units is the development of a mathematical model that can adequately record the processes at any time. The operative and accurate measurement of all input and output variables is one of the important conditions in the development of a mathematical model of technological processes. Studies have shown that the lack of information about the state of complex oil refining processes in many cases reduces their efficiency and effectiveness. On the other hand, th

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16

Victorov, Alexey S., and Olga N. Trapeznikova. "Stochastic Models Of Dynamic Balance State For The Morphological Patterns Of Cryolithozone Landscapes." GEOGRAPHY, ENVIRONMENT, SUSTAINABILITY 12, no. 3 (October 3, 2019): 6–15. http://dx.doi.org/10.24057/2071-9388-2018-68.

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The paper deals with mathematical modeling of a morphological pattern for a broad spectrum of cryolithozone landscapes in a state of a dynamic balance. The state of the dynamic balance means that all the elements of this morphological pattern are in continuous changing while its general parameters as a whole are stable. Two contradirectional processes at the same territory is a precondition for a state of dynamic balance.We developed a morphological pattern model for lacustrine thermokarst plains with fluvial erosion on the base of the mathematical morphology of landscape using the random proc

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17

Artikis, Constantinos T., and Panagiotis T. Artikis. "Processes of educational informatics incorporating stochastic models." Journal of Interdisciplinary Mathematics 12, no. 4 (August 2009): 553–64. http://dx.doi.org/10.1080/09720502.2009.10700646.

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18

Batchelder, William H., and John P. Boyd. "Models for behavior: Stochastic processes in psychology." Journal of Mathematical Psychology 29, no. 1 (March 1985): 122–27. http://dx.doi.org/10.1016/0022-2496(85)90022-7.

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19

Diosi, L. "Quantum stochastic processes as models for state vector reduction." Journal of Physics A: Mathematical and General 21, no. 13 (July 7, 1988): 2885–98. http://dx.doi.org/10.1088/0305-4470/21/13/013.

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20

Schall, Jeffrey D., Thomas J. Palmeri, and Gordon D. Logan. "Models of inhibitory control." Philosophical Transactions of the Royal Society B: Biological Sciences 372, no. 1718 (February 27, 2017): 20160193. http://dx.doi.org/10.1098/rstb.2016.0193.

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We survey models of response inhibition having different degrees of mathematical, computational and neurobiological specificity and generality. The independent race model accounts for performance of the stop-signal or countermanding task in terms of a race between GO and STOP processes with stochastic finishing times. This model affords insights into neurophysiological mechanisms that are reviewed by other authors in this volume. The formal link between the abstract GO and STOP processes and instantiating neural processes is articulated through interactive race models consisting of stochastic

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21

Maccone, Claudio. "Evolution and mass extinctions as lognormal stochastic processes." International Journal of Astrobiology 13, no. 4 (July 21, 2014): 290–309. http://dx.doi.org/10.1017/s147355041400010x.

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AbstractIn a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely calledEvo-SETI. The relevant mathematical tools are:(1)Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black–Sholes models). Its main features are th

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22

Duso, Lorenzo, and Christoph Zechner. "Stochastic reaction networks in dynamic compartment populations." Proceedings of the National Academy of Sciences 117, no. 37 (August 31, 2020): 22674–83. http://dx.doi.org/10.1073/pnas.2003734117.

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Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populatio

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23

CARNAFFAN, SEAN. "ANOMALOUS DIFFUSION PROCESSES: STOCHASTIC MODELS AND THEIR PROPERTIES." Bulletin of the Australian Mathematical Society 101, no. 3 (March 27, 2020): 514–17. http://dx.doi.org/10.1017/s0004972720000258.

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24

LOWEN, STEVEN B., and MALVIN C. TEICH. "ESTIMATION AND SIMULATION OF FRACTAL STOCHASTIC POINT PROCESSES." Fractals 03, no. 01 (March 1995): 183–210. http://dx.doi.org/10.1142/s0218348x95000151.

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We investigate the properties of fractal stochastic point processes (FSPPs). First, we define FSPPs and develop several mathematical formulations for these processes, showing that over a broad range of conditions they converge to a particular form of FSPP. We then provide examples of a wide variety of phenomena for which they serve as suitable models. We proceed to examine the analytical properties of two useful fractal dimension estimators for FSPPs, based on the second-order properties of the points. Finally, we simulate several FSPPs, each with three specified values of the fractal dimensio

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25

Pfeiffer, F., and A. Kunert. "Rattling models from deterministic to stochastic processes." Nonlinear Dynamics 1, no. 1 (January 1990): 63–74. http://dx.doi.org/10.1007/bf01857585.

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26

WEIDLICH, WOLFGANG. "SOCIODYNAMICS — A SYSTEMATIC APPROACH TO MATHEMATICAL MODELLING IN THE SOCIAL SCIENCES." Fluctuation and Noise Letters 03, no. 02 (June 2003): L223—L232. http://dx.doi.org/10.1142/s0219477503001294.

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A general concept is presented which allows of setting up mathematical models for stochastic and quasi deterministic dynamic processes in social systems. The basis of this concept is the master equation for the probability distribution over appropriately chosen personal and material macrovariables of the society. The probabilistic transition rates depend on motivation potentials governing the decisions and actions of the social agents. The transition from the probability distribution to quasi-meanvalues leads to in general nonlinear coupled differential equations for the macrovariables of the

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27

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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28

COSTANTINI, CRISTINA, and THOMAS G. KURTZ. "DIFFUSION APPROXIMATION FOR TRANSPORT PROCESSES WITH GENERAL REFLECTION BOUNDARY CONDITIONS." Mathematical Models and Methods in Applied Sciences 16, no. 05 (May 2006): 717–62. http://dx.doi.org/10.1142/s0218202506001339.

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Diffusion approximations are obtained for space inhomogeneous linear transport models with reflection boundary conditions. The collision kernel is not required to satisfy any balance condition and the scattering kernel on the boundary is general enough to include all examples of boundary conditions known to the authors (with conservation of the number of particles) and, in addition, to model the Debye sheath. The mathematical approach does not rely on Hilbert expansions, but rather on martingale and stochastic averaging techniques.

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29

Cordoni, Francesco, and Luca Di Persio. "Backward Stochastic Differential Equations Approach to Hedging, Option Pricing, and Insurance Problems." International Journal of Stochastic Analysis 2014 (September 11, 2014): 1–11. http://dx.doi.org/10.1155/2014/152389.

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In the present work we give a self-contained introduction to financial mathematical models characterized by noise of Lévy type in the framework of the backward stochastic differential equations theory. Such techniques will be then used to analyse an innovative model related to insurance and death processes setting.

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30

Lazarova, Meglena Delcheva, Krasimira Prodanova, and Leda Minkova. "Research Project DN 12/11/December 2017-January 2022 financed by the National Science Fund at the Ministry of Education and Science: "Stochastic and Simulation Models in medcine, social sciences and dynamic systems"." Biomath Communications 9, no. 1 (February 16, 2022): 1. http://dx.doi.org/10.11145/bmc.2022.02.161.

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The project " Stochastics and Simulation Models in the Medcine, Social Sciences and Dynamical Systems" is focused on the stochastic models and their applications in the field of medicine, insurance, astrophysics and some simulation models applicable in social sciences and thermotydraulic processes. There are six work packages included in the research. The introduced models had been adapted to real data by three phd students, two post doctoral students and four Bulgarian scientists which are leaders in the field of mathematical modeling. The participants' research results are published in eight

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31

Lobato, Lucas C., Stephan Paul, Júlio A. Cordioli, and Thiago G. Ritto. "Stochastic model of the human middle ear using a nonparametric probabilistic approach." Journal of the Acoustical Society of America 151, no. 3 (March 2022): 2055–65. http://dx.doi.org/10.1121/10.0009763.

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Several mathematical models of the human middle ear dynamics have been studied since the mid-twentieth century. Despite different methods applied, all of these models are based on deterministic approaches. Experimental data have shown that the middle ear behaves as an uncertain system due to the variability among individuals. In this context, stochastic models are useful because they can represent a population of middle ears with its intrinsic uncertainties. In this work, a nonparametric probabilistic approach is used to model the human middle ear dynamics. The lumped-element method is adopted

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32

Hughes-Oliver, Jacqueline M., and Graciela González-Farı́as. "Parametric covariance models for shock-induced stochastic processes." Journal of Statistical Planning and Inference 77, no. 1 (February 1999): 51–72. http://dx.doi.org/10.1016/s0378-3758(98)00186-4.

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33

Hwan Cha, Ji, and Sophie Mercier. "Transformed Lévy processes as state-dependent wear models." Advances in Applied Probability 51, no. 2 (June 2019): 468–86. http://dx.doi.org/10.1017/apr.2019.21.

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AbstractMany wear processes used for modeling accumulative deterioration in a reliability context are nonhomogeneous Lévy processes and, hence, have independent increments, which may not be suitable in an application context. In this work we consider Lévy processes transformed by monotonous functions to overcome this restriction, and provide a new state-dependent wear model. These transformed Lévy processes are first observed to remain tractable Markov processes. Some distributional properties are derived. We investigate the impact of the current state on the future increment level and on the

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34

Loomis, Samuel P., and James P. Crutchfield. "Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes." Journal of Statistical Physics 176, no. 6 (June 26, 2019): 1317–42. http://dx.doi.org/10.1007/s10955-019-02344-x.

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35

Lee, Mei-Ling Ting, and G. Alex Whitmore. "Stochastic processes directed by randomized time." Journal of Applied Probability 30, no. 2 (June 1993): 302–14. http://dx.doi.org/10.2307/3214840.

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The paper investigates stochastic processes directed by a randomized time process. A new family of directing processes called Hougaard processes is introduced. Monotonicity properties preserved under subordination, and dependence among processes directed by a common randomized time are studied. Results for processes subordinated to Poisson and stable processes are presented. Potential applications to shock models and threshold models are also discussed. Only Markov processes are considered.

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36

Velichkin, Vladimir, Vladimir Zavyalov, Elena Solodovnikova, and Elena Filippova. "Mathematical descriptions of heat-mass-exchange processes in construction industry at control automation." E3S Web of Conferences 97 (2019): 06021. http://dx.doi.org/10.1051/e3sconf/20199706021.

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The paper covers matters arising in building mathematical model of processes at thermal treatment of construction materials. On the basis of analysis of heat energy and moisture flows in intermittent steam chamber and continuous tunnel drying chamber, analytic and structure models of heat-mass-exchange processes in processing vessels are drawn. The structural model of heat-mass-exchange processes allowed to evaluate the relationship of heat energy and moisture flows at heat treatment processes for gypsum and reinforced-concrete articles. The resulting system of interrelated differential equati

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37

Etchegaray, Christèle, and Nicolas Meunier. "A Stochastic Model For Protrusion Activity." ESAIM: Proceedings and Surveys 62 (2018): 56–67. http://dx.doi.org/10.1051/proc/201862056.

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In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a function of the (discrete) protrusive forces exerted by filopodia on the substrate. Cell polarisation ability is modeled in the feedback that the cell motion exerts on the protrusion rates: faster cells form preferentially protrusions in the direction of motion. By using the mathematical framework of structured population processes previously developed to stu

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38

Otunuga, Olusegun M., and Gangaram Ladde. "Two-Scale Network Dynamic Model for Energy Commodity Processes." Journal of Energy 2020 (April 20, 2020): 1–59. http://dx.doi.org/10.1155/2020/2075258.

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In this work, we examine the relationship between different energy commodity spot prices. To do this, multivariate stochastic models with and without external random interventions describing the price of energy commodities are developed. Random intervention process is described by a continuous jump process. The developed mathematical model is utilized to examine the relationship between energy commodity prices. The time-varying parameters in the stochastic model are estimated using the recently developed parameter identification technique called local lagged adapted generalized method of momen

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39

Chigarev, Anatoliy V., Michael A. Zhuravkov, and Vitaliy A. Chigarev. "Deterministic and stochastic models of infection spread and testing in an isolated contingent." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (November 19, 2021): 57–67. http://dx.doi.org/10.33581/2520-6508-2021-3-57-67.

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The mathematical SIR model generalisation for description of the infectious process dynamics development by adding a testing model is considered. The proposed procedure requires the expansion of states’ space dimension due to variables that cannot be measured directly, but allow you to more adequately describe the processes that occur in real situations. Further generalisation of the SIR model is considered by taking into account randomness in state estimates, forecasting, which is achieved by applying the stochastic differential equations methods associated with the application of the Fokker

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40

Aase, Knut K. "Stochastic control of geometric processes." Journal of Applied Probability 24, no. 1 (March 1987): 97–104. http://dx.doi.org/10.2307/3214062.

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Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.

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Aase, Knut K. "Stochastic control of geometric processes." Journal of Applied Probability 24, no. 01 (March 1987): 97–104. http://dx.doi.org/10.1017/s0021900200030643.

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Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.

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42

Andriyanov, Nikita A., Madina-Bonu R. Atakhodzhaeva, and Evgeny I. Borodin. "Mathematical modeling of recommender system and data processing of a telecommunications company using machine learning models." Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control & Radioelectronics 22, no. 2 (April 2022): 17–28. http://dx.doi.org/10.14529/ctcr220202.

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The purpose of the study is to develop data modeling methods for projecting recommender algorithms using doubly stochastic autoregressive models of random processes and checking their adequacy by applying machine learning algorithms to cluster users in a simulated data set and predict probabilities of interest. Research methods. The article discusses the methods used in the construction of recommender systems. At the same time, the problem of modeling user behavior using a doubly stochastic model is considered. This model is proposed for generating artificial data. The doubly stochastic model

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43

Filatov, V. O., A. L. Yerokhin, O. V. Zolotukhin, and M. S. Kudryavtseva. "Hybrid simulation models for complex decision-making problems with partial uncertainty." Information extraction and processing 2022, no. 50 (December 19, 2022): 78–86. http://dx.doi.org/10.15407/vidbir2022.50.078.

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Specific features of application of hybrid simulation and control models in information systems and system support for decision-making in solving practical problems under conditions of uncertainty, vagueness, inaccuracy, stochasticity of processes of subject areas are considered. To obtain reliable data, it is necessary to use poorly formalized operational and long-term data on the state of the object of control, expert knowledge, application of mathematical programming methods with stochastic or fuzzy constraints, as well as many cause-and-effect relations between processes that may be presen

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44

Warne, David J., Ruth E. Baker, and Matthew J. Simpson. "Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art." Journal of The Royal Society Interface 16, no. 151 (February 2019): 20180943. http://dx.doi.org/10.1098/rsif.2018.0943.

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Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealizations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour

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Dumont, Grégory, Jacques Henry, and Carmen Oana Tarniceriu. "A theoretical connection between the Noisy Leaky integrate-and-fire and the escape rate models: The non-autonomous case." Mathematical Modelling of Natural Phenomena 15 (2020): 59. http://dx.doi.org/10.1051/mmnp/2020017.

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Finding a mathematical model that incorporates various stochastic aspects of neural dynamics has proven to be a continuous challenge. Among the different approaches, the noisy leaky integrate-and-fire and the escape rate models are probably the most popular. These two models are generally thought to express different noise action over the neural cell. In this paper we investigate the link between the two formalisms in the case of a neuron subject to a time dependent input. To this aim, we introduce a new general stochastic framework. As we shall prove, our general framework entails the two alr

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Cairoli, Andrea, Rainer Klages, and Adrian Baule. "Weak Galilean invariance as a selection principle for coarse-grained diffusive models." Proceedings of the National Academy of Sciences 115, no. 22 (May 14, 2018): 5714–19. http://dx.doi.org/10.1073/pnas.1717292115.

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How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invari

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Linde, W. "STABLE NON-GAUSSIAN RANDOM PROCESSES: STOCHASTIC MODELS WITH INFINITE VARIANCE." Bulletin of the London Mathematical Society 28, no. 5 (September 1996): 554–56. http://dx.doi.org/10.1112/blms/28.5.554.

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TSENG, JIE-JUN, MING-JER LEE, and SAI-PING LI. "HEAVY-TAILED DISTRIBUTIONS IN FATAL TRAFFIC ACCIDENTS: ROLE OF HUMAN ACTIVITIES." International Journal of Modern Physics C 20, no. 08 (August 2009): 1281–90. http://dx.doi.org/10.1142/s0129183109014345.

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Human activities can play a crucial role in the statistical properties of observables in many complex systems such as social, technological, and economic systems. We demonstrate this by looking into the heavy-tailed distributions of observables in fatal plane and car accidents. Their origin is examined and can be understood as stochastic processes that are related to human activities. Simple mathematical models are proposed to illustrate such processes and compared with empirical results obtained from existing databanks.

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Potapova, Nadin, Lyudmila Volontyr, and Oksana Zelinska. "MATHEMATICAL AND STATISTICAL EVALUATION OF PROCESSES OF USING INFORMATION TECHNOLOGIES." ENGINEERING, ENERGY, TRANSPORT AIC, no. 4(111) (December 18, 2020): 61–71. http://dx.doi.org/10.37128/2520-6168-2020-4-7.

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The article covers the methodological issues of mathematical and statistical evaluation of the information technology use. The necessity of using information technologies to ensure control system flexibility has been substantiated. The impact of the level of integration of implemented information technologies on the increase of production management efficiency through data processing models and use of a single information space has been determined. To achieve the appropriate characteristics of stochastic processes of information technology, it is proposed to use methodological approaches to mo

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Lawson, Michael J., Linda Petzold, and Andreas Hellander. "Accuracy of the Michaelis–Menten approximation when analysing effects of molecular noise." Journal of The Royal Society Interface 12, no. 106 (May 2015): 20150054. http://dx.doi.org/10.1098/rsif.2015.0054.

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Quantitative biology relies on the construction of accurate mathematical models, yet the effectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis–Menten (MM) approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, owing to the ubiquity of enzymatic activity in cellular processes and the clear biochemical interpretation of its parameters. However, it is not well understood how the approximation applies to the discrete stoch

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