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Nonlinear Trend Exclusion Procedure for Models defined by Stochastic Differential and Difference Equations
Automation and Remote Control. 2017. Vol. 78. No. 8. P. 1438–1448.
Konakov V., Markova A.
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 considered for a Markov chain.
Keywords: цепи МарковаMarkov chaindiffusion processesдиффузионный процессметод параметриксаstochastic differential equationsстохастические дифференциальные уравненияSDEparametrix method
Publication based on the results of:
Bitter I., Konakov V., / Cornell University. Серия arXiv "math". 2025. № 2505.24548.
В работе приводится обобщение локальной предельной теоремы о сходимости неоднородных цепей Маркова к диффузионному пределу на случай, когда соответ- ствующие коэффициенты процессов удовлетворяют слабым условиям регулярности и совпадают лишь асимптотически. В частности, рассматриваемые нами коэффици- енты сноса могут быть неограниченными с не более чем линейным ростом, а оценки отражают перенос терминального состояния неограниченным трендом через ...
Added: December 3, 2025
Магазев А. А., Касенов А. А., Трапезников Е. В., Моделирование, оптимизация и информационные технологии 2024 Т. 12 № 2 (45)
The paper presents a description of the Markov model of cyber attacks as a method for analyzing information security in automated systems. Based on the presented model, the work provides a description of two safety metrics - the average time to safety failure (the average number of transitions between states in the corresponding Markov chain ...
Added: September 26, 2025
Sheshukova M., Belomestny D., Durmus A. et al., , in: Proceedings of the 13th International Conference on Learning Representations (ICLR 2025).: ICLR, 2025.
Added: August 15, 2025
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
Bitter I., Управление большими системами: сборник трудов 2025 № 113 С. 6–20
Выводится локальная предельная теорема для возмущенных выборочных траекторий нормализованных сумм индуцированных порядковых статистик, полученных из последовательности независимых одинаково распределенных случайных векторов при слабых условиях регулярности на коэффициенты. Рассматриваемая ситуация является типовым примером задачи оценки скорости сходимости дискретных по времени марковских процессов к диффузиям, когда соответствующие тренды и коэффициенты диффузии марковской цепи и диффузионного предела совпадают ...
Added: May 2, 2025
Sheshukova M., Belomestny D., Durmus A. et al., / Series arXiv "math". 2024.
We address the problem of solving strongly convex and smooth minimization problems using stochastic gradient descent (SGD) algorithm with a constant step size. Previous works suggested to combine the Polyak-Ruppert averaging procedure with the Richardson-Romberg extrapolation technique to reduce the asymptotic bias of SGD at the expense of a mild increase of the variance. We ...
Added: October 13, 2024
Lyulko Y., Theory of Probability and Its Applications 2012 Vol. 56 No. 1 P. 140–149
Added: August 28, 2024
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
Fedotov I. A., A. S. Khritankov, Obidare M. D., Programming and Computer Software 2023 Vol. 49 No. 5 P. 448–454
Multi-party agreements are used in distributed ledger systems and blockchain networks to reach an agreement on changes in the system. When one of the network participants proposes a transaction to be recorded, it should be first confirmed by certain network participants. A multi-party agreement or consensus determines who exactly these participants are. Based on the ...
Added: October 9, 2023
A.I. Nurieva, A.Yu. Veretennikov, Reliability: Theory & Applications 2022 Vol. 17 No. 4(71) P. 521–529
The consistency of the Bayesian estimation of a parameter is shown for a class of ergodic discrete Markov chains. J.L. Doob’s method was used, offered earlier for the i.i.d. situation. The result may be useful in the reliability theory for models with unknown parameters, in the risk management in financial mathematics, and in other applications. ...
Added: October 8, 2023
Durmus A., Moulines E., Naumov A. et al., / Series arXiv "math". 2023.
In this paper, we establish novel deviation bounds for additive functionals of geometrically ergodic Markov chains similar to Rosenthal and Bernstein-type inequalities for sums of independent random variables. We pay special attention to the dependence of our bounds on the mixing time of the corresponding chain. Our proof technique is, as far as we know, ...
Added: June 18, 2023
E. M. Khayrov, V. A. Prosvirov, Platonova A., , in: Distributed Computer and Communication Networks: Control, Computation, Communications: 25th International Conference, DCCN 2022, Moscow, Russia, September 26–29, 2022, Revised Selected Papers.: Switzerland: Springer, 2022. Ch. 13 P. 161–175.
The introduction of integrated access and backhaul (IAB) technology in beyond 5G systems will result in multiple wireless backhaul links between the user equipment (UE) and the base station (BS). This configuration motivates the research into traffic at the packet level to evaluate the quality of service (QoS) provided to users. At the same time, ...
Added: May 19, 2023
Konakov V., Mammen E., / Series arXiv "math". 2023. No. 2304.10673.
The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate the zeros of a function that can be written as an expectation. It is known that under some technical assumptions, Gaussian limit distributions approximate the stochastic performance of the algorithm. Here, we are interested in strong approximations for Robbins-Monro procedures. The main tool for ...
Added: April 24, 2023
Samsonov S., Lagutin E., Gabrie M. et al., , in: Thirty-Sixth Conference on Neural Information Processing Systems : NeurIPS 2022.: Curran Associates, Inc., 2022. P. 5178–5193.
Added: February 1, 2023
Cardoso G., Samsonov S., Thin A. et al., , in: Thirty-Sixth Conference on Neural Information Processing Systems : NeurIPS 2022.: Curran Associates, Inc., 2022. P. 716–729.
Added: February 1, 2023
Царев А. С., Хайров Э. М., Гайдамака Ю. В. et al., Системы и средства информатики 2021 Т. 31 № 2 С. 16–25
Industrial Internet of Things (IIoT) is one of the key features of Industry 4.0 that stands for a new approach to design industrial processes using the latest technological advances. However, before implementing new processes, it is necessary to understand the characteristics and limitations that arise due to technical complexity of the system. To solve this ...
Added: December 12, 2022
Minsk: [б.и.], 2022.
This collection of papers includes proceedings of the Thirteenth International Conference "Computer Data Analysis and Modeling: Stochastics and Data Science" organized by the Belarusian State University and held in September 2022 in Minsk. Papers are reviewed by qualied researchers from Belarus and Russia. ...
Added: October 27, 2022
Durmus A., Moulines E., Naumov A. et al., Mathematics of Operations Research 2025 Vol. 50 No. 2 P. 935–964
This paper provides a finite-time analysis of linear stochastic approximation (LSA) algorithms with fixed step size, a core method in statistics and machine learning. LSA is used to compute approximate solutions of a $d$-dimensional linear system $\bar{\mathbf{A}} \theta = \bar{\mathbf{b}}$, for which $(\bar{\mathbf{A}}, \bar{\mathbf{b}})$ can only be estimated through (asymptotically) unbiased observations $\{(\mathbf{A}(Z_n),\mathbf{b}(Z_n))\}_{n \in \mathbb{N}}$. ...
Added: July 13, 2022
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
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
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