Dmitry Dolgopyat's Books

Local Limit Theorems for Inhomogeneous Markov Chains

By: Dmitry Dolgopyat,Omri M. Sarig

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Local Limit Theorems for Inhomogeneous Markov Chains

By: Dmitry Dolgopyat,Omri M. Sarig

This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.

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Page Count

348

Publisher

Springer Nature

Published Date

ISBN 10

3031326016

ISBN 13

9783031326011

Brownian Brownian Motion-I

By: Nikolai Chernov,Dmitry Dolgopyat

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Brownian Brownian Motion-I

By: Nikolai Chernov,Dmitry Dolgopyat

A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work the authors study a 2D version of this model, where the molecule is a heavy disk of mass $M \gg 1$ and the gas is represented by just one point particle of mass $m=1$, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of the particles is ensured by convex (scattering) walls of the container. The authors prove that the position and velocity of the disk, in an appropriate time scale, converge, as $M\to\infty$, to a Brownian motion (possibly, inhomogeneous); the scaling regime and the structure of the limit process depend on the initial conditions. The proofs are based on strong hyperbolicity of the underlying dynamics, fast decay of correlations in systems with elastic collisions (billiards), and methods of averaging theory.

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Page Count

208

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082184282X

ISBN 13

9780821842829

Geometric and Probabilistic Structures in Dynamics

Workshop on Dynamical Systems and Related Topics in Honor of Michael Brin on the Occasion of His 60th Birthday, March 15-18, 2008, University of Maryland, College Park, MD

By: Keith Burns,Dmitry Dolgopyat,Ya. B. Pesin

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Geometric and Probabilistic Structures in Dynamics

Workshop on Dynamical Systems and Related Topics in Honor of Michael Brin on the Occasion of His 60th Birthday, March 15-18, 2008, University of Maryland, College Park, MD

By: Keith Burns,Dmitry Dolgopyat,Ya. B. Pesin

This book presents a collection of articles that cover areas of mathematics related to dynamical systems. The authors are well-known experts who use geometric and probabilistic methods to study interesting problems in the theory of dynamical systems and its applications. Some of the articles are surveys while others are original contributions. The topics covered include: Riemannian geometry, models in mathematical physics and mathematical biology, symbolic dynamics, random and stochastic dynamics. This book can be used by graduate students and researchers in dynamical systems and its applications."--BOOK JACKET.

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Page Count

358

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821842862

ISBN 13

9780821842867

Local Limit Theorems for Inhomogeneous Markov Chains

By: Dmitry Dolgopyat,Omri M. Sarig

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Local Limit Theorems for Inhomogeneous Markov Chains

By: Dmitry Dolgopyat,Omri M. Sarig

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Solve jigsaw puzzle

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Page Count

348

Publisher

Springer Nature

Published Date

ISBN 10

3031326016

ISBN 13

9783031326011

Brownian Brownian Motion-I

By: Nikolai Chernov,Dmitry Dolgopyat

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Brownian Brownian Motion-I

By: Nikolai Chernov,Dmitry Dolgopyat

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N/A

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Solve jigsaw puzzle

Age

Page Count

208

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082184282X

ISBN 13

9780821842829

Book's by Dmitry Dolgopyat

Local Limit Theorems for Inhomogeneous Markov Chains

Local Limit Theorems for Inhomogeneous Markov Chains

Brownian Brownian Motion-I

Brownian Brownian Motion-I

Geometric and Probabilistic Structures in Dynamics

Geometric and Probabilistic Structures in Dynamics

Local Limit Theorems for Inhomogeneous Markov Chains

Local Limit Theorems for Inhomogeneous Markov Chains

Brownian Brownian Motion-I

Brownian Brownian Motion-I

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