2025/01/23 by Juho Leppänen, Leppänen, Juho, Y. Nakajima +3
Economics, Econometrics and Finance · Mathematics · #37A05 #37A50 #60F17 #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2501.13498
openalex publication_date 2025/01/23 · openalex created_date 2025/01/25 · openalex updated_date 2026/07/31
We adapt Stein's method of diffusion approximations, developed by Barbour, to the study of chaotic dynamical systems. We establish an error bound in the functional central limit theorem with respect to an integral probability metric of smooth test functions under a functional correlation decay bound. For systems with a sufficiently fast polynomial rate of correlation decay, the error bound is of order O(N-1/2), under an additional condition on the linear growth of variance. Applications include a family of interval maps with neutral fixed points and unbounded derivatives, and two-dimensional dispersing Sinai billiards.