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Wasserstein convergence rates in the invariance principle for deterministic dynamical systems

Part of: Ergodic theory Limit theorems Dynamical systems with hyperbolic behavior Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  13 June 2023

ZHENXIN LIU  and
ZHE WANG
ZHENXIN LIU
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China (e-mail: zxliu@dlut.edu.cn)
ZHE WANG*
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China (e-mail: zxliu@dlut.edu.cn)
*
e-mail: zwangmath@hotmail.com, wangz1126@mail.dlut.edu.cn
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Abstract

In this paper, we consider the convergence rate with respect to Wasserstein distance in the invariance principle for deterministic non-uniformly hyperbolic systems. Our results apply to uniformly hyperbolic systems and large classes of non-uniformly hyperbolic systems including intermittent maps, Viana maps, unimodal maps and others. Furthermore, as a non-trivial application to the homogenization problem, we investigate the Wasserstein convergence rate of a fast–slow discrete deterministic system to a stochastic differential equation.

Keywords

invariance principlerate of convergenceWasserstein distancenon-uniformly hyperbolic systemhomogenization

MSC classification

Primary: 37A50: Relations with probability theory and stochastic processes 60F17: Functional limit theorems; invariance principles
Secondary: 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 60B10: Convergence of probability measures

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 4 , April 2024 , pp. 1172 - 1191
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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