Stein's method for dynamical systems

We present an adaptation of Stein's method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical systems for a multivariate central limit theorem augmented by a rate of convergence. We then present a...

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Bibliographic Details
Published in:arXiv.org 2017-01
Main Authors: Hella, Olli, Leppänen, Juho, Stenlund, Mikko
Format: Article
Language:English
Subjects:
Convergence
Dynamical systems
Theorems
Online Access:Get full text
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Summary:We present an adaptation of Stein's method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical systems for a multivariate central limit theorem augmented by a rate of convergence. We then present a scheme for checking these conditions in actual examples. The principal contribution of our paper is the method, which yields a convergence rate essentially with the same amount of work as the central limit theorem, together with a multiplicative constant that can be computed directly from the assumptions.
ISSN:2331-8422