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Towards Multi-Dimensional Nonlinear Langevin Equation
P. 278–283.
Lubashevsky I.
The work is devoted to possible generalizations of the Langevin equation based on the notion of the intermediate point determining the contribution of nonlinear random forces and different channels of noise action.
In book
Kyoto: The Institute of Systems, Control and Information Engineers , 2014.
Kolokoltsov V., Electronic Journal of Probability 2025 Vol. 30 Article 57
Stochastic Master equations or quantum filtering equations for mixed states are well known objects in quantum physics. Building a mathematically rigorous theory of these equations in infinite-dimensional spaces has been a long standing open problem. The first objective of this paper is to give a solution to this problem under the assumption of bounded operators ...
Added: May 29, 2025
Lubashevsky I., Lubashevskiy V., Computer Research and Modeling 2024 Vol. 16 No. 1 P. 79–87
We present a novel model for the dynamical trap of the stimulus-response type that mimics human control over dynamic systems when the bounded capacity of human cognition is a crucial factor. Our focus lies on scenarios where the subject modulates a control variable in response to a certain stimulus. In this context, the bounded capacity ...
Added: February 25, 2024
Sirota V. A., Ilyin A., Kopyev A. V. et al., Physics of Fluids 2024 Vol. 36 No. 2 Article 021701
A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow and can be expressed in terms of local surface densities. The expression for the integrals is universal: it represents general geometric properties ...
Added: February 17, 2024
Stoop R., Orlando G., Bufalo M. et al., Scientific Reports 2022 Vol. 12 No. 1 Article 19843
Many processes in nature are the result of many coupled individual subsystems (like population
dynamics or neurosystems). Not always such systems exhibit simple stable behaviors that in the
past science has mostly focused on. Often, these systems are characterized by bursts of seemingly
stochastic activity, interrupted by quieter periods. The hypothesis is that the presence of a strong
deterministic ...
Added: June 27, 2023
Korolev A. V., , in: Frontiers of Dynamic Games: Game Theory and Management, St. Petersburg, 2020.: Cham: Birkhäuser, 2021. P. 167–187.
Added: April 5, 2022
Lubashevsky I., The European Physical Journal B 2010 Vol. 82 P. 189–195
A continuous Markovian model for truncated Lévy flights is proposed. It generalizes the approach developed previously by Lubashevsky et al. [Phys. Rev. E 79, 011110 (2009); Phys. Rev. E 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010)] and allows for nonlinear friction in wandering particle motion as well as saturation of the noise intensity ...
Added: November 6, 2021
Kyoto: The Institute of Systems, Control and Information Engineers , 2014.
Added: November 5, 2021
Lubashevsky I., Mahnke R., Kaupuzs J., Weinheim: Wiley-VCH, 2009.
Based on lectures given by one of the authors with many years of experience in teaching stochastic processes, this textbook is unique in combining basic mathematical and physical theory with numerous simple and sophisticated examples as well as detailed calculations. In addition, applications from different fields are included so as to strengthen the background learned in ...
Added: November 5, 2021
Veretennikov A., Modern Stochastics: Theory and Applications 2021 Vol. 8 No. 1 P. 1–15
Several methods of establishing coupling for stochastic differential equations are presented. ...
Added: August 29, 2021
Korolev A. V., Математическая теория игр и ее приложения 2021 № 1 С. 102–129
In this paper, stochastic parameters are introduced into the network games model with production and knowledges externalities. This model was formulated by V. Matveenko and A. Korolev and generalized two-period Romer model. Agents' productivities have deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle which ...
Added: May 15, 2021
Korolev A. V., , in: Frontiers of Dynamic Games Game Theory and Management, St. Petersburg, 2019.: Birkhauser/Springer, 2020. Ch. 6 P. 65–85.
In this paper we introduce stochastic parameters into the network game
model with production and knowledge externalities. This model was proposed
by V. Matveenko and A. Korolev as a generalization of the two-period Romer
model. Agents differ in their productivities which have deterministic and stochastic
(Wiener) components. We study the dynamics of a single agent and the dynamics
of a ...
Added: November 30, 2020
Birkhauser/Springer, 2020.
The content of this volume is mainly based on selected talks that were given at the
“International Meeting on Game Theory (ISDG12-GTM2019),” as joint meeting of
“12th International ISDG Workshop” and “13th International Conference on Game
Theory and Management,” held in St. Petersburg, Russia on July 03–05, 2019. The
meeting was organized by St. Petersburg State University and International ...
Added: November 30, 2020
Gostev I. M., Геворкян М., Демидова А. et al., В кн.: Материалы Всероссийской конференции с международным участием ИНФОРМАЦИОННО- ТЕЛЕКОММУНИКАЦИОННЫЕ ТЕХНОЛОГИИ И МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ВЫСОКОТЕХНОЛОГИЧНЫХ СИСТЕМ.: М.: Издательство РУДН, 2018. С. 318–320.
This article discusses stochastic numerical methods of Runge-Kutta type with weak and strong convergences for systems of stochastic differential equations in Itô form. At the beginning we give a brief overview of the stochastic numerical methods and information from the theory of stochastic differential equations. Then we motivate the approach to the implementation of these ...
Added: December 19, 2018
Konakov V., Markova A., Automation and Remote Control 2017 Vol. 78 No. 8 P. 1438–1448
We consider the diffusion process and its approximation by Markov chain with nonlinear unbounded trends. The usual parametrix method is not applicable because these models have unbounded trends. We describe a procedure that allows to exclude nonlinear unbounded trend and move to stochastic differential equation with bounded drift and diffusion coefficients. A similar procedure is ...
Added: August 28, 2017
Konakov V., Markova A., Automation and Remote Control 2015 Vol. 76 No. 10 P. 1771–1783
We consider a sequence of Markov chains that weakly converge to a diffusion process. We assume that the trend contains a linearly growing component. The usual parametrix method does not apply since the trend is unbounded. We show how to modify the parametrix method in order to get local limit theorems in this case. ...
Added: October 23, 2015
Konakov V., Markova A., / Series math "arxiv.org". 2014. No. 1412.1607v1.
We consider a sequence of Markov chains weakly convergent to a diffusion. We suppose that a drift term contains a linearly increasing component. The usual parametrix method fails because of this unbounded drift term. We show how to modify the parametrix method to obtain local theorems for this case. ...
Added: January 21, 2015
Gushchin A. A., Küchler U., Bernoulli: a journal of mathematical statistics and probability 2001 Vol. 7 No. 4 P. 629–632
We strengthen the convergence result in our paper, ibid. 5, No. 6, 1059-1098 (1999; Zbl 0983.62049), proving the local asymptotic mixed normality property in one of the 11 cases considered in that paper. ...
Added: October 9, 2013