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Проблемы реализации стохастических численных методов Рунге–Кутты
С. 318-320.
Gostev I. M., Геворкян М., Демидова А., Кулябов Д. С.
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 methods using source code generation. We discuss the implementation details and the used programming languages and libraries
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
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
Many heads but one brain: FusionBrain – a single multimodal multitask architecture and a competition
D. D. Bakshandaeva, Dimitrov D. V., Arkhipkin V. S. et al., Computer Optics 2023 Vol. 47 No. 1 P. 185-195
Supporting the current trend in the AI community, we present the AI Journey 2021 Challenge called FusionBrain, the first competition which is targeted to make a universal architecture which could process different modalities (in this case, images, texts, and code) and solve multiple tasks for vision and language. The FusionBrain Challenge combines the following specific tasks: Code2code ...
Added: June 13, 2023
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., 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
Soshnikov D. V., Valieva Y., / Cornell University. Series Computer Science "arxiv.org". 2021.
In this paper, we present a new Python library called mPyPl, which is intended to simplify complex data processing tasks using functional approach. This library defines operations on lazy data streams of named dictionaries represented as generators (so-called multi-field datastreams), and allows enriching those data streams with more 'fields' in the process of data preparation ...
Added: October 7, 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
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
Il'in A. S., Копьев А., Сирота В. А. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2022 Vol. 105 No. 5 Article 9
We consider finite-dimensional systems of linear stochastic differential equations ∂txk(t)=Akp(t)xp(t), A(t) being a stationary continuous statistically isotropic stochastic process with values in real d×d matrices. We suppose that the laws of A(t) satisfy the large-deviation principle. For these systems, we find exact expressions for the Lyapunov and generalized Lyapunov exponents and show that they are determined in a precise way only by ...
Added: May 20, 2022
Аслаханов А. Р., Pavlova E., Логистика и управление цепями поставок 2020 № 4 (99) С. 29-38
In recent years, both in Russia and in the world, there has been an annual increase in the number of museum visitors. The most popular exhibitions are visited by millions of people. In 2020, in the context of quarantine measures caused by the COVID-19 epidemic, the issue of managing the museum's visitors’ flows has become ...
Added: September 29, 2020
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
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
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
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
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
Volkova O. N., Вологина Д. -., Korolev A. V., Математическая теория игр и ее приложения 2022 Т. 14 № 1 С. 21-48
Вводятся стохастические параметры в модели сетевых игр с производством и экстерналиями знаний, которая была сформулирована В. Матвеенко и А. Королевым и обобщает двухпериодную модель Ромера. Агенты различаются продуктивностью, имеющей детерминированную и винеровскую составляющие. Рассматривается динамика, которая возникает при объединении двух полных сетей. Получены явные выражения в форме броуновских случайных процессов. Проведен качественный анализ решения системы ...
Added: May 11, 2022
Konakov V., Markova A., / Cornell University. 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
Veretennikov A., Клоков С. А., Теория вероятностей и ее применения 2012 Т. 57 № 1 С. 35-61
Построены аппроксимации решения стохастического дифференциального уравнения при минимальных условиях гладкости коэффициента сноса. ...
Added: October 18, 2014
Lubashevsky I., , in : Proceedings of the 45th ISCIE International Symposium on Stochastic Systems Theory and Its Applications. : Kyoto : The Institute of Systems, Control and Information Engineers , 2014. P. 278-283.
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. ...
Added: November 5, 2021