Veretennikov, A (2017) Ergodic Markov Processes and Poisson Equations (Lecture Notes). In: Panov, V, (ed.) Springer Proceedings in Mathematics and Statistics. MPSAS 2016: Modern Problems of Stochastic Analysis and Statistics, 29 May - 02 Jun 2016, Moscow, Russia. Springer International Publishing , Cham, Switzerland , pp. 457-511. ISBN 978-3-319-65312-9
Abstract
These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, perhaps, except for the Sect. 10 about Poisson equations with potentials; also, the convergence rate shown in (83)–(84) is possibly less known. Yet, the hope of the author is that these notes may serve as a bridge to the important area of Poisson equations ‘in the whole space’ and with a parameter, the latter theme not being presented here. Why this area is so important was explained in many papers and books including (Ethier and Kurtz, Markov Processes: Characterization and Convergence, New Jersey, 2005) [12], (Papanicolaou et al. Statistical Mechanics, Dynamical Systems and the Duke Turbulence Conference, vol. 3. Durham, N.C., 1977) [34], (Pardoux and Veretennikov, Ann. Prob. 31(3), 1166–1192, 2003) [35]: it provides one of the main tools in diffusion approximation in the area stochastic averaging. Hence, the aim of these lectures is to prepare the reader to ‘real’ Poisson equations—i.e. for differential operators instead of difference operators—and, indeed, to diffusion approximation. Among other presented topics, we mention coupling method and convergence rates in the Ergodic theorem.
Metadata
Item Type: | Proceedings Paper |
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Copyright, Publisher and Additional Information: | © Springer International Publishing AG 2017. This is the peer reviewed version of the following article: Veretennikov A. (2017) Ergodic Markov Processes and Poisson Equations (Lecture Notes). In: Panov V. (eds) Modern Problems of Stochastic Analysis and Statistics. MPSAS 2016. Springer Proceedings in Mathematics & Statistics, vol 208. Springer, Cham, which has been published in final form at https://doi.org/10.1007/978-3-319-65313-6_18. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Markov chains; Ergodic theorem; Limit theorems; Coupling; Discrete poisson equations |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Apr 2017 11:55 |
Last Modified: | 13 Jun 2022 13:58 |
Status: | Published |
Publisher: | Springer International Publishing |
Identification Number: | 10.1007/978-3-319-65313-6_18 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:115261 |