Stein's method for dynamical systems

2017/01/11 by Olli Hella, Hella, Olli, Juho Leppänen +3
Computer Science · Mathematics · Physics and Astronomy · #37A05 #37A50 #60F05 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum chaos and dynamical systems #Topological and Geometric Data Analysis #math-ph #math.DS #math.MP #math.PR #msc:37A05 #msc:37A50 #msc:60F05

paper · pdf · doi:10.48550/arxiv.1701.02966

arxiv created 2017/01/11 · openalex publication_date 2017/01/11 · arxiv updated 2017/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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