Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the central limit theorem for dynamical systems


Authors: Robert Burton and Manfred Denker
Journal: Trans. Amer. Math. Soc. 302 (1987), 715-726
MSC: Primary 60F05; Secondary 28D05
DOI: https://doi.org/10.1090/S0002-9947-1987-0891642-6
MathSciNet review: 891642
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given an aperiodic dynamical system $(X,T,\mu )$ then there is an $f \in {L^2}(\mu )$ with $\smallint fd\mu = 0$ satisfying the Central Limit Theorem, i.e. if ${S_m}f = f + f \circ T + \cdots + f \circ {T^{m - 1}}$ and ${\sigma _m} = {\left \| {{S_m}f} \right \|_2}$ then \[ \mu \left \{ {x|\frac {{{S_m}f(x)}}{{{\sigma _m}}} < u} \right \} \to {(2\pi )^{ - 1/2}}\int _{ - \infty }^u {{\text {exp}}} \left [ {\frac {{ - {\upsilon ^2}}}{2}} \right ]d\upsilon .\] The analogous result also holds for flows.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60F05, 28D05

Retrieve articles in all journals with MSC: 60F05, 28D05


Additional Information

Keywords: Central limit theorem, dynamical systems
Article copyright: © Copyright 1987 American Mathematical Society