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Journal articles on the topic 'Chapman-Kolmogorov equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

TARASOV, VASILY E. "THE FRACTIONAL CHAPMAN–KOLMOGOROV EQUATION." Modern Physics Letters B 21, no. 04 (2007): 163–74. http://dx.doi.org/10.1142/s0217984907012712.

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The Chapman–Kolmogorov equation with fractional integrals is derived. An integral of fractional order is considered as an approximation of the integral on fractal. Fractional integrals can be used to describe the fractal media. Using fractional integrals, the fractional generalization of the Chapman–Kolmogorov equation is obtained. From the fractional Chapman–Kolmogorov equation, the Fokker–Planck equation is derived.

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2

FRANK, T. D. "NUMERIC AND EXACT SOLUTIONS OF THE NONLINEAR CHAPMAN–KOLMOGOROV EQUATION: A CASE STUDY FOR A NONLINEAR SEMI-GROUP MARKOV MODEL." International Journal of Modern Physics B 23, no. 19 (2009): 3829–43. http://dx.doi.org/10.1142/s0217979209053497.

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Nonlinear Markov processes are known to arise from diffusion approximations of nonlinear master equations and generalized Boltzmann equations and have been studied in their own merit in the context of nonlinear Fokker–Planck equations. Nonlinear Markov processes can account for collective phenomena, collective oscillations, and collective chaotic behavior. Despite the importance of nonlinear Markov processes for the physics of stochastic processes, relatively little is known about the Chapman–Kolmogorov equation of nonlinear Markov processes. The manuscript derives the exact solution of the Ch

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3

Lee, Wha-Suck, and Niko Sauer. "Intertwined Markov processes: the extended Chapman–Kolmogorov equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 1 (2017): 123–31. http://dx.doi.org/10.1017/s0308210517000075.

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Uniformization transforms a pseudo-Poisson process with unequal intensities (leaving rates) into one with uniform intensity. Self-transitions is the price to pay. Two intensities arise when one considers an absorbing barrier of a Markov process as a body in its own right: a pair of Markov processes intertwined by an extended Chapman–Kolmogorov equation naturally arises. We show that Sauer's two-state space empathy theory handles such intertwined processes. The price of self-transitions is also avoided.

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4

Miroshin, R. N. "On some solutions to the Chapman-Kolmogorov integral equation." Vestnik St. Petersburg University: Mathematics 40, no. 4 (2007): 253–59. http://dx.doi.org/10.3103/s1063454107040012.

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5

Courbage, M., and D. Hamdan. "Chapman-Kolmogorov Equation for Non-Markovian Shift-Invariant Measures." Annals of Probability 22, no. 3 (1994): 1662–77. http://dx.doi.org/10.1214/aop/1176988618.

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6

Myers-Beaghton, A. K., and D. D. Vvedensky. "Chapman-Kolmogorov equation for Markov models of epitaxial growth." Journal of Physics A: Mathematical and General 22, no. 11 (1989): L467—L475. http://dx.doi.org/10.1088/0305-4470/22/11/004.

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7

Hierro, Juan, and César Dopazo. "Singular Boundaries in the Forward Chapman-Kolmogorov Differential Equation." Journal of Statistical Physics 137, no. 2 (2009): 305–29. http://dx.doi.org/10.1007/s10955-009-9842-x.

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8

Metzler, Ralf, and Joseph Klafter. "From a Generalized Chapman−Kolmogorov Equation to the Fractional Klein−Kramers Equation†." Journal of Physical Chemistry B 104, no. 16 (2000): 3851–57. http://dx.doi.org/10.1021/jp9934329.

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9

IIZUKA, Masaru, Miyuki MAENO, and Matsuyo TOMISAKI. "Conditional distributions which do not satisfy the Chapman-Kolmogorov equation." Journal of the Mathematical Society of Japan 59, no. 4 (2007): 971–83. http://dx.doi.org/10.2969/jmsj/05940971.

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10

Nicolis, G., S. Martínez, and E. Tirapegui. "Finite coarse-graining and Chapman-Kolmogorov equation in conservative dynamical systems." Chaos, Solitons & Fractals 1, no. 1 (1991): 25–37. http://dx.doi.org/10.1016/0960-0779(91)90053-c.

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11

Cai, Yuzhi. "Convergence Theory of a Numerical Method for Solving the Chapman--Kolmogorov Equation." SIAM Journal on Numerical Analysis 40, no. 6 (2002): 2337–51. http://dx.doi.org/10.1137/s0036142901390366.

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12

Cocozza-Thivent, Christiane, Robert Eymard, Sophie Mercier, and Michel Roussignol. "Characterization of the marginal distributions of Markov processes used in dynamic reliability." Journal of Applied Mathematics and Stochastic Analysis 2006 (March 5, 2006): 1–18. http://dx.doi.org/10.1155/jamsa/2006/92156.

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In dynamic reliability, the evolution of a system is described by a piecewise deterministic Markov process (It,Xt)t≥0 with state-space E×ℝd, where E is finite. The main result of the present paper is the characterization of the marginal distribution of the Markov process (It,Xt)t≥0 at time t, as the unique solution of a set of explicit integro-differential equations, which can be seen as a weak form of the Chapman-Kolmogorov equation. Uniqueness is the difficult part of the result.

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13

Breuer, Heinz-Peter, and Francesco Petruccione. "Stochastic dynamics of open quantum systems: Derivation of the differential Chapman-Kolmogorov equation." Physical Review E 51, no. 5 (1995): 4041–54. http://dx.doi.org/10.1103/physreve.51.4041.

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14

Dallagi, A., J. Forbes, M. G. Forbes, and M. Guay. "Stochastic feedforward—feedback control design in a discrete-time case." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 222, no. 7 (2008): 655–60. http://dx.doi.org/10.1243/09596518jsce573.

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This paper examines the role of random feedforward inputs in a probabilistic framework for stochastic control design in a discrete-time case. Fundamental rules of probability are applied to extend the Chapman—Kolmogorov equation by including the effect of the additional random disturbance variables. The steady state solution to this equation is then applied to the design of two long-term regulatory controllers: a probability-density-shaping controller and an approximation of an optimal controller with respect to a non-symmetric and non-quadratic cost functions.

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15

BATUNIN, A. V., and O. P. YUSHCHENKO. "PARTON RECOMBINATION IN CLASSICAL CASCADE." Modern Physics Letters A 05, no. 28 (1990): 2377–83. http://dx.doi.org/10.1142/s0217732390002730.

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An equation for parton multiplicity in cascade with the recombination 1 → 2 ⊕ 2 → 1 is derived from a Kolmogorov-Chapman equation and solved. An evolution parameter τ of the cascade depends on the c.m. energy [Formula: see text]; an explicit form of the dependence is obtained from the condition that the mean multiplicity of charged particles in pp, [Formula: see text] collisions be reproduced. A considerable decrease in the mean multiplicity in heavy-ion collisions per pair of the colliding nucleons at high energies is predicted and compared to the parton cascade with no recombination.

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16

Bahl, Yakshi, and Tarun Kumar Garg. "Measurement and improvement of efficiency of Library by mathematical modelling and finding reliability." VEETHIKA-An International Interdisciplinary Research Journal 7, no. 2 (2021): 1–5. http://dx.doi.org/10.48001/veethika.2021.07.02.001.

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Here in this paper we have developed the mathematical model of the library server using Markov birth – death process assuming that library system server system is based on exponential distribution. The model so developed by victimisation Chapman Kolmogorov differential equation and is solved by using Mathematica. The solution so obtained is analysed for various rates of failures and repair. The finding so obtained are discussed with the concerned authorities of the library to boost the efficiency of the library.

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17

Miroshin, R. N. "On the solution of the Chapman-Kolmogorov integral equation in the form of a series." Vestnik St. Petersburg University: Mathematics 42, no. 2 (2009): 130–34. http://dx.doi.org/10.3103/s1063454109020095.

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18

Miroshin, R. N. "On some solutions of Chapman-Kolmogorov equation for discrete-state Markov processes with continuous time." Vestnik St. Petersburg University: Mathematics 43, no. 2 (2010): 63–67. http://dx.doi.org/10.3103/s1063454110020019.

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19

Miroshin, R. N. "Special solutions of the Chapman–Kolmogorov equation for multidimensional-state Markov processes with continuous time." Vestnik St. Petersburg University: Mathematics 49, no. 2 (2016): 122–29. http://dx.doi.org/10.3103/s1063454116020114.

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20

SZABŁOWSKI, PAWEŁ J. "PROBABILISTIC IMPLICATIONS OF SYMMETRIES OF q-HERMITE AND AL-SALAM–CHIHARA POLYNOMIALS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 04 (2008): 513–22. http://dx.doi.org/10.1142/s0219025708003257.

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We prove the existence of stationary random fields with linear regressions for q > 1 and thus close an open question posed by W. Bryc et al. We prove this result by describing a discrete one-dimensional conditional distribution and then checking Chapman–Kolmogorov equation. Support of this distribution consists of zeros of certain Al-Salam–Chihara polynomials. To find them we refer to and expose known result concerning addition of q-exponential function. This leads to generalization of a well-known formula [Formula: see text], where Hk(x) denotes kth Hermite polynomial.

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21

Strumik, M., and W. M. Macek. "Statistical analysis of transfer of fluctuations in solar wind turbulence." Nonlinear Processes in Geophysics 15, no. 4 (2008): 607–13. http://dx.doi.org/10.5194/npg-15-607-2008.

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Abstract. We present results of statistical analysis of the transfer of fluctuations in solar wind turbulence. We investigate the dynamics of the slow solar wind using an approach based on the Markov processes theory and experimental data measured by ACE spacecraft. In particular, we test whether the Chapman-Kolmogorov equation is approximately satisfied for the turbulent cascade. We consider the following cases of transfer of fluctuations: magnetic-to-magnetic, velocity-to-velocity, velocity-to-magnetic, and magnetic-to-velocity. In all these cases, the obtained results confirm local characte

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22

Imomkulov, Anvar, and Victoria Velasco. "Chains of three-dimensional evolution algebras: A description." Filomat 34, no. 10 (2020): 3175–90. http://dx.doi.org/10.2298/fil2010175i.

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In this paper we describe locally all the chains of three-dimensional evolution algebras (3-dimensional CEAs). These are families of evolution algebras with the property that their structure matrices with respect to a certain natural basis satisfy the Chapman-Kolmogorov equation. We do it by describing all 3-dimensional CEAs whose structure matrices have a fixed rank equal to 3, 2 and 1, respectively. We show that arbitrary CEAs are locally CEAs of fixed rank. Since every evolution algebra can be regarded as a weighted digraph, this allows us to understand and visualize time-dependent weighted

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23

Miroshin, Roman N. "Particular solutions of the Chapman—Kolmogorov equation for multi-dimensional-state Markov process with continuous time." Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy 3 (61), no. 2 (2016): 212–20. http://dx.doi.org/10.21638/11701/spbu01.2016.205.

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24

Metzler, Ralf. "Generalized Chapman-Kolmogorov equation: A unifying approach to the description of anomalous transport in external fields." Physical Review E 62, no. 5 (2000): 6233–45. http://dx.doi.org/10.1103/physreve.62.6233.

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25

Iwankiewicz, Radosław. "Response of dynamic systems to renewal impulse processes: Generating equation for moments based on the integro-differential Chapman–Kolmogorov equations." Probabilistic Engineering Mechanics 35 (January 2014): 52–66. http://dx.doi.org/10.1016/j.probengmech.2013.10.006.

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26

GHASEMI, FATEMEH, J. PEINKE, M. REZA RAHIMI TABAR, and MUHAMMAD SAHIMI. "STATISTICAL PROPERTIES OF THE INTERBEAT INTERVAL CASCADE IN HUMAN HEARTS." International Journal of Modern Physics C 17, no. 04 (2006): 571–80. http://dx.doi.org/10.1142/s0129183106008704.

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Statistical properties of interbeat intervals cascade in human hearts are evaluated by considering the joint probability distribution P (Δx2, τ2; Δx1, τ1) for two interbeat increments Δx1and Δx2of different time scales τ1and τ2. We present evidence that the conditional probability distribution P (Δx2, τ2| Δx1, τ1) may be described by a Chapman–Kolmogorov equation. The corresponding Kramers–Moyal (KM) coefficients are evaluated. The analysis indicates that while the first and second KM coefficients take on well-defined and significant values, the higher-order coefficients in the KM expansion ar

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27

Wang, Hongjian, Cun Li, Ying Wang, Qing Li, and Xicheng Ban. "A New State Estimation Method with Radar Measurement Missing." Complexity 2018 (December 2, 2018): 1–10. http://dx.doi.org/10.1155/2018/5327637.

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This paper describes a method that addresses the transient loss of observations in sea surface target state estimations. A six degrees of freedom swing platform fixed with a MiniRadaScan is used to simulate the loss of observations. The state transition model based on the historical observation data fit prediction is designed because the existing state estimation method can only use the system model prediction while the observation is missing. An observation data sliding window width adaptive adjustment strategy is proposed that can improve the fitting accuracy of the state transition model. T

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28

AKINTUNDE, A. A., S. O. N. AGWUEGBO, and O. M. OLAYIWOLA. "MARKOV MODELS FOR THE ANALYSIS OF DYNAMICAL SYSTEMS." Journal of Natural Sciences Engineering and Technology 16, no. 1 (2017): 35–49. http://dx.doi.org/10.51406/jnset.v16i1.1801.

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Most real world situations involve modelling of physical processes that evolve with time and space, especially those exhibiting high variability. Such events that have to flow with time or space are called dynamical systems. The mathematical notions of a dynamical system serves to depict the flow of causation from past into future (Kalman 1960). In this study, Markov model which is a signal model based on the Markovian property with state space approach was adopted for the analysis of dynamical systems. The Nigerian monetary exchange rate data was used in the application with the use of R stat

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29

Tyagi, Manav, and Patrick Jenny. "Probability density function approach for modelling multi-phase flow with ganglia in porous media." Journal of Fluid Mechanics 688 (October 17, 2011): 219–57. http://dx.doi.org/10.1017/jfm.2011.374.

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AbstractA probabilistic approach to model macroscopic behaviour of non-wetting-phase ganglia or blobs in multi-phase flow through porous media is proposed. The key idea is to consider a set of stochastic Markov processes that can mimic the microscopic multi-phase dynamics. These processes are characterized by equilibrium probability density functions (PDFs) and correlation times, which can be obtained from micro-scale simulation studies or experiments. A Lagrangian viewpoint is adopted, where stochastic particles represent infinitesimal fluid elements and evolve in the physical and probability

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30

Iwankiewicz, Radosław. "Integro-differential Chapman–Kolmogorov equation for continuous-jump Markov processes and its use in problems of multi-component renewal impulse process excitations." Probabilistic Engineering Mechanics 26, no. 1 (2011): 16–25. http://dx.doi.org/10.1016/j.probengmech.2010.06.002.

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31

Eden, Uri T., Loren M. Frank, Riccardo Barbieri, Victor Solo, and Emery N. Brown. "Dynamic Analysis of Neural Encoding by Point Process Adaptive Filtering." Neural Computation 16, no. 5 (2004): 971–98. http://dx.doi.org/10.1162/089976604773135069.

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Neural receptive fields are dynamic in that with experience, neurons change their spiking responses to relevant stimuli. To understand how neural systems adapt the irrepresentations of biological information, analyses of receptive field plasticity from experimental measurements are crucial. Adaptive signal processing, the well-established engineering discipline for characterizing the temporal evolution of system parameters, suggests a framework for studying the plasticity of receptive fields. We use the Bayes' rule Chapman-Kolmogorov paradigm with a linear state equation and point process obse

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32

Kamal, Md Sarwar, and Mohammad Ibrahim Khan. "Chapman–Kolmogorov equations for global PPIs with Discriminant-EM." International Journal of Biomathematics 07, no. 05 (2014): 1450053. http://dx.doi.org/10.1142/s1793524514500533.

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Ongoing improvements in Computational Biology research have generated massive amounts of Protein–Protein Interactions (PPIs) dataset. In this regard, the availability of PPI data for several organisms provoke the discovery of computational methods for measurements, analysis, modeling, comparisons, clustering and alignments of biological data networks. Nevertheless, fixed network comparison is computationally stubborn and as a result several methods have been used instead. We illustrate a probabilistic approach among proteins nodes that are part of various networks by using Chapman–Kolmogorov (

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33

Barendregt, Nicholas W., Krešimir Josić, and Zachary P. Kilpatrick. "Analyzing dynamic decision-making models using Chapman-Kolmogorov equations." Journal of Computational Neuroscience 47, no. 2-3 (2019): 205–22. http://dx.doi.org/10.1007/s10827-019-00733-5.

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34

Siergiejczyk, Mirosław, and Adam Rosiński. "Analysis of Power Supply Maintenance in Transport Telematics System." Solid State Phenomena 210 (October 2013): 14–19. http://dx.doi.org/10.4028/www.scientific.net/ssp.210.14.

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Issues concerning maintenance of power-supply for transport telematics systems were presented in this paper. Relationships graph was presented, and then Chapman–Kolmogorov system of equations was derived to describe it. Drawing on those equations, relationships for calculating function of probability of system staying in state of full ability SPZ, state of the impendency over safety SZB1and SZB2as well as state of unreliability of safety SBwere derived.

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35

Alfa, Attahiru Sule, and T. S. S. Srinivasa Rao. "SUPPLEMENTARY VARIABLE TECHNIQUE IN STOCHASTIC MODELS." Probability in the Engineering and Informational Sciences 14, no. 2 (2000): 203–18. http://dx.doi.org/10.1017/s0269964800142068.

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In this article, we formalize the framework for the supplementary variable technique in stochastic models. Specifically, we show that the use of remaining or elapsed times (or any metric) as supplementary variables leads to the notion of forward or backward Chapman–Kolmogorov equations, respectively. We further show that for a class of queueing systems, using remaining time as the supplementary variable makes analysis simpler.

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36

Radak, Branislav. "Chapman–Kolmogorov equations for multi-period equity-linked note with conditional coupons." International Journal of Financial Engineering 04, no. 01 (2017): 1750009. http://dx.doi.org/10.1142/s2424786317500098.

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An equity-linked note with complex payoff and a path dependent variable maturity is analyzed analytically and numerically. This note pays up to one coupon, the size of which depends on the period count in which it is paid and with initial investment partially protected. Valuation of this instrument is achieved in closed form in terms of multivariate normal distribution function, but simple, fast and accurate numerical solution in terms of Chapman–Kolmogorov equations is preferred. The note has a number of unique features, some of which expose the investors to types of risk not usually encounte

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37

Matsena Zingoni, Zvifadzo, Tobias F. Chirwa, Jim Todd, and Eustasius Musenge. "A review of multistate modelling approaches in monitoring disease progression: Bayesian estimation using the Kolmogorov-Chapman forward equations." Statistical Methods in Medical Research 30, no. 5 (2021): 1373–92. http://dx.doi.org/10.1177/0962280221997507.

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There are numerous fields of science in which multistate models are used, including biomedical research and health economics. In biomedical studies, these stochastic continuous-time models are used to describe the time-to-event life history of an individual through a flexible framework for longitudinal data. The multistate framework can describe more than one possible time-to-event outcome for a single individual. The standard estimation quantities in multistate models are transition probabilities and transition rates which can be mapped through the Kolmogorov-Chapman forward equations from th

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38

Rosiński, Adam. "Rationalisation of the Operation Process of Power Supply Systems of Highway Telematics." Applied Mechanics and Materials 817 (January 2016): 253–60. http://dx.doi.org/10.4028/www.scientific.net/amm.817.253.

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The paper presents the issues related to the operation of the operation process of the power supply system of highway telematics. A relationships graph was presented in the considered system, and the Kolmogorov-Chapman system of equations was derived to describe it. Drawing on those equations, relationships for calculating probability of the power supply system staying in state of complete usability SPZ, state of the impendency over safety SZB as well as the state of unreliability of safety SB were derived. Next, this enabled rationalisation of the operation process of the analysed systems.

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39

Siergiejczyk, Mirosław, Jacek Paś, and Adam Rosiński. "Reliability And Maintenance Analysis Of CCTV Systems Used In Rail Transport." Journal of KONBiN 35, no. 1 (2015): 137–46. http://dx.doi.org/10.1515/jok-2015-0047.

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Abstract CCTV systems are widely used across plethora of industrial areas including transport, where their function is to support transport telematics systems. Among others, they are used to ensure travel safety. This paper presented a reliability and maintenance analysis of CCTV. It led to building a relationships graph and then Chapman–Kolmogorov system of equations was derived to describe it. Drawing on those equations, relationships for calculating probability of system staying in state of full ability SPZ, state of the impendency over safety SZB1 as well as state of unreliability of safet

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40

ZVEREV, V. V. "NOISE TRANSFORMATION IN NONLINEAR SYSTEM WITH INTENSITY DEPENDENT PHASE ROTATION." Stochastics and Dynamics 03, no. 04 (2003): 421–33. http://dx.doi.org/10.1142/s0219493703000814.

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The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov–Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the external noise perturbations. We find a stationary solution in the long-time limit as a power series around a state with complete phase randomization ("phase mixing"). The Ornstein–Uhlenbeck and Kubo–Andersen models of noise statistics are considered; the conditions of convergence of the power expansions are established.

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41

Veshneva, I., and G. Chernyshova. "The scenario modeling of regional competitiveness risks based on the Chapman-Kolmogorov equations." Journal of Physics: Conference Series 1784, no. 1 (2021): 012008. http://dx.doi.org/10.1088/1742-6596/1784/1/012008.

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42

Siergiejczyk, Mirosław, Karolina Krzykowska, and Adam Rosiński. "Reliability-exploitation analysis of the alarm columns of highway emergency communication system / Analiza niezawodnościowo-eksploatacyjna kolumn alarmowych autostradowego systemu łączności alarmowej." Journal of KONBiN 38, no. 1 (2016): 53–76. http://dx.doi.org/10.1515/jok-2016-0018.

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Abstract The article presents issues concerning on the alarm columns of highway emergency communication system. The system is presented in general and then the reliability-exploitation analysis was done. This enabled preparing a development graph of the relationship, under which is created a set of Kolmogorov-Chapman equations describing the system. On this basis, it was possible to find the relation for calculating the probabilities of system staying (in symbolic terms) in the functional: states of full ability SPZ, impendency over safety SZB and unreliability of safety SB.

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43

SZCZEPAŃSKI, Paweł, and Józef ŻUREK. "Chapman-Kolmogorov Equations for a Complete Set of Distinct Reliability States of an Object." Problems of Mechatronics Armament Aviation Safety Engineering 9, no. 4 (2018): 49–70. http://dx.doi.org/10.5604/01.3001.0012.7332.

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The Chapman-Kolmogorov equations indicated in the title are a pretext to demonstrate a mathematically unrecognised truth about the effect of the reliability states of elements (which are generally understood as “subjects”) on the reliability states of a complete set of the same elements, which is called an object. Of importance here are not just the reliability characteristics of individual elements, but the independencies, dependencies and interdependencies between the elements. The relations were described in the language of graph theory. The availability matrix of the language of graph theo

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44

Rosiński, Adam. "Reliability analysis of the power supply system of closed-circuit television system used at a highway toll collection point." Journal of KONBiN 41, no. 1 (2017): 39–58. http://dx.doi.org/10.1515/jok-2017-0003.

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Abstract The article presents issues concerning the power supply systems of closed-circuit television systems used at a highway toll collection point. The general diagram of the power supply system was presented, and then the reliability analysis was conducted. This enabled to develop a relationships graph, on the basis of which the Chapman–Kolmogorov system of equations describing it was created. On this basis, it was possible to set the relationships allowing to calculate the probability values of the system’s staying (in symbolic terms) in the following functional states: of full ability SP

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45

Nánási, Tibor. "Availability and Productivity of Simple Production Chains." Applied Mechanics and Materials 309 (February 2013): 12–19. http://dx.doi.org/10.4028/www.scientific.net/amm.309.12.

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Stochastic Markov process is formulated for a system of independent production machines with few redundant units in cold, warm or hot standby regime. The disposable repair capacity is restricted. Resulting system of Kolmogorov-Chapman differential equations is solved numerically for different configurations of the production system. Time evolution is relatively insensitive on the renewal capacity and the number of redundant units. The steady state is completely determined by the ratio of failure and the repair rate. Effectiveness of the system as measured by the volume of production is markedl

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46

KALETA, KAMIL, MARIUSZ OLSZEWSKI, and KATARZYNA PIETRUSKA-PAŁUBA. "REFLECTED BROWNIAN MOTION ON SIMPLE NESTED FRACTALS." Fractals 27, no. 06 (2019): 1950104. http://dx.doi.org/10.1142/s0218348x19501044.

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For a large class of planar simple nested fractals, we prove the existence of the reflected diffusion on a complex of an arbitrary size. Such a process is obtained as a folding projection of the free Brownian motion from the unbounded fractal. We give sharp necessary geometric conditions for the fractal under which this projection can be well defined, and illustrate them by numerous examples. We then construct a proper version of the transition probability densities for the reflected process and we prove that it is a continuous, bounded and symmetric function which satisfies the Chapman–Kolmog

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Lipovetsky, Stan. "MaxDiff Choice Probability Estimations on Aggregate and Individual Level." International Journal of Business Analytics 5, no. 1 (2018): 55–69. http://dx.doi.org/10.4018/ijban.2018010104.

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This paper considers methods of estimation of choice probability using Maximum Difference (MaxDiff) technique, also known as Best-Worst Scaling (BWS). The paper shows that on the aggregate level the choice probabilities can be obtained using analytical closed-form solution and other approaches such as Thurstone scaling, Bradley-Terry maximum likelihood, and Markov modeling via Chapman-Kolmogorov equations for steady-states probabilities. On the individual level, to account for the exact combinations presented in each task, the Cox hazard model is employed, as well as new approaches of least sq

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LIPOVETSKY, STAN. "BRADLEY–TERRY CHOICE PROBABILITY IN MAXIMUM LIKELIHOOD AND EIGENPROBLEM SOLUTIONS." International Journal of Information Technology & Decision Making 07, no. 03 (2008): 395–405. http://dx.doi.org/10.1142/s0219622008003010.

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The Bradley–Terry model (BT) is commonly used for evaluation of choice preferences by paired comparison data in various areas of applied psychology, advertising, and marketing research. The estimation of BT parameters of preference is usually achieved in an iterative procedure based on the maximum likelihood approach. In this paper an easier way of finding these parameters via an eigenproblem is considered. This approach corresponds to solving a Chapman–Kolmogorov system of equations to estimate the steady-state probabilities of the compared items. Both techniques produce very similar results,

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Veshneva1, Irina V., Galina Yu Chernyshova, and Alexander A. Bolshakov. "AN INTELLIGENT INFORMATION SYSTEM DESIGN FOR ANALYSIS AND PREDICTION OF THE DYNAMICS OF RISKS OF THE COMPETITIVENESS OF REGIONS OF THE RUSSIAN FEDERATION." Bulletin of the Saint Petersburg State Institute of Technology (Technical University) 56 (2021): 81–88. http://dx.doi.org/10.36807/1998-9849-2020-56-82-81-88.

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It was revealed that there are no generally accepted methods for assessing competitiveness; modern research is mainly a theoretical analysis of regional competitiveness. It was substantiated that the use of mathematical models and quantitative methods will improve the objectivity of the assessment. A methodology for an information system design for analysis and prediction of the dynamics of risks of competitiveness of regions of the Russian Federation was proposed. The prospects and directions of intellectualization of that system were shown. Based on the analysis of officially published stati

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Lipovetsky, Stan, and W. Michael Conklin. "Choice Models Adjusted to Non-Available Items and Network Effects." International Journal of Business Analytics 6, no. 1 (2019): 1–19. http://dx.doi.org/10.4018/ijban.2019010101.

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Discrete choice modeling is one of the main tools of estimation utilities and preference probabilities among multiple alternatives in economics, psychology, social sciences, and marketing research. One of popular DCM tools is the Best-Worst Scaling, also known as Maximum Difference. Data for such modeling is given by respondents presented with several items, and each respondent chooses the best alternative. Estimation of utilities is usually performed in a multinomial-logit modeling which produces utilities and choice probabilities. This article describes how to obtain probability estimation a

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