?
Ergodic Markov processes and Poisson equations (lecture notes)
P. 457–511.
Ergodic properties of Markov chains are studied, with the emphasis to convergence rate bounds and to applications to Poisson equations
Publication based on the results of:
In book
Heidelberg: Springer, 2017.
Veretennikov A., Markov Processes and Related Fields 2023 Vol. 23 No. 2 P. 259–294
The ergodic Bellman's (HJB) equation is proved for a one-dimensional controlled diffusion with switching with variable diffusion and drift coefficients both depending on control; the intensities of transitions of the discrete component are constant. Its existence and uniqueness is established. Also, the convergence of the reward iteration improvement algorithm is established to the cost constant ...
Added: July 16, 2026
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
Lyulko Y., Theory of Probability and Its Applications 2012 Vol. 56 No. 1 P. 140–149
Added: August 28, 2024
Dynnikov I., Hubert P., Skripchenko A., International Mathematics Research Notices 2023 Vol. 2023 No. 8 P. 6461–6503
At the beginning of the 80s, H. Masur and W. Veech started the study of generic properties of interval exchange transformations (IETs) proving that almost every such transformation is uniquely ergodic. About the same time, S. Novikov’s school and French mathematicians independently discovered very intriguing phenomena for classes of measured foliations on surfaces and respective ...
Added: December 28, 2023
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
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
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
Veretennikov A., Veretennikova M., Известия РАН. Серия математическая 2022 Т. 86 № 1 С. 98–133
We continue the work of improving the rate of convergence of ergodic homogeneous Markov chains. The setting is more general than in previous papers: we are able to get rid of the assumption about a common dominating measure and consider the case of inhomogeneous Markov chains as well as more general state spaces. We give examples ...
Added: March 14, 2022
Suvorkov P., В кн.: Демография и этнокультурная география: тенденции развития в современном мире.: Псков: Издательство Псковского государственного университета, 2021. С. 16–23.
The article discusses a number of non-trivial research aspects that arise in the process of developing models of ethnodemographic forecasting. The purpose of the article is to study the properties of weak ergodicity to substantiate express assessments of the reproductive potential of ethnic groups. ...
Added: November 29, 2021
Aleksandr A. Shchegolev, Random Operators and Stochastic Equations 2022 Vol. 30 No. 3 P. 205–213
In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition steps. An example of a class such a process provided indicates that such types of estimates considering several transition steps may ...
Added: October 30, 2021
Khaymovich I. M., Kravtsov V. E., Altshuler B. L. et al., Physical Review Research 2020 Vol. 2 P. 1–21
In this paper, we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We argue that this model is more suitable to describe a generic many-body localization problem. In contrast to RP model, in LN-RP model, a fragile weakly ergodic phase appears ...
Added: September 24, 2021
Shchegolev A., Управление большими системами: сборник трудов 2021 № 90 С. 36–48
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the current probability distributions of the process apart from being dependent on the current state. Such processes often act as limits ...
Added: April 21, 2021
Zlotnik A.A., Zlotnik I.A., Computational Mathematics and Mathematical Physics 2020 Vol. 60 No. 2 P. 240–257
We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor products finite element method (FEM) based on the tensor products of the 1D high-order FEM spaces on multi-dimensional rectangular parallelepipeds for solving the $N$-dimensional Poisson type equation $-\Delta u+\alpha u=f$ ($N\geq 2$) with the Dirichlet boundary conditions. They are based ...
Added: May 19, 2020
Gordin V. A., В кн.: Современные проблемы математического моделирования: сборник трудов XVIII Всероссийской конференции-школы молодых исследователей (пос. Абрау-Дюрсо, 16–20 сентября 2019 г.).: Ростов н/Д: Издательство ЮФУ, 2019. Гл. 9 С. 40–52.
When solving boundary value problems of mathematical physics, compact schemes allow increasing (in comparison with classical ones) the solution accuracy order with a slight increase in the number of arithmetic operations. An indispensable condition of the algorithm is the use of the double-sweep approach. A method for calculating the coefficients of schemes is shown both ...
Added: December 30, 2019
Гордин В.А., Шадрин Д. А., В кн.: Современные проблемы математического моделирования: сборник трудов XVIII Всероссийской конференции-школы молодых исследователей (пос. Абрау-Дюрсо, 16–20 сентября 2019 г.).: Ростов н/Д: Издательство ЮФУ, 2019. Гл. 10 С. 53–57.
The boundary value problem for the Poisson and Helmholtz equations with a piecewise constant coefficient with a jump on a triangle is studied numerically. At the jump of the coefficient (at the boundary of the media), the docking conditions are set. A compact difference scheme with high accuracy with a relatively small number of calculations ...
Added: December 30, 2019
Veretennikov A., Theory of Probability and Mathematical Statistics 2017 Vol. 95 P. 195–206
Poisson equation n the whole space is solved for a generator of a diffusion process with a potential which may change sign. ...
Added: December 6, 2019
Veretennikov A., Veretennikova M., / Series "Working papers by Cornell University". 2019.
New convergence rate asymptotic bound for a class of homogeneous Markov chains is established. ...
Added: November 14, 2019
Grabchak M., Kelbert M., Paris Q., Journal of Applied Probability 2020 Vol. 57 No. 1 P. 53–77
This article studies the expected occupancy probabilities on an alphabet. Unlike
the standard situation, where observations are assumed to be independent and identically
distributed (iid), we assume that they follow a regime switching Markov chain. For
this model, we 1) give finite sample bounds on the occupancy probabilities, and 2) provide
detailed asymptotics in the case where the underlying ...
Added: November 13, 2019
Moltchanov D., Ometov A., Koucheryavy E., Computer Communications 2019 No. 146 P. 110–120
One of the recent major steps towards 5G cellular systems is standardization of 5G New Radio (NR) operatingin the millimeter wave (mmWave) frequency band. This radio access technology (RAT) will potentially provideextraordinary rates at the access interface enabling the set of new bandwidth-greedy applications. However,the blockage of the line-of-sight (LoS) path between 3GPP NR access ...
Added: October 31, 2019