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July 2010 Almost sure invariance principle for dynamical systems by spectral methods
Sébastien Gouëzel
Ann. Probab. 38(4): 1639-1671 (July 2010). DOI: 10.1214/10-AOP525

Abstract

We prove the almost sure invariance principle for stationary ℝd-valued random processes (with very precise dimension-independent error terms), solely under a strong assumption concerning the characteristic functions of these processes. This assumption is easy to check for large classes of dynamical systems or Markov chains using strong or weak spectral perturbation arguments.

Citation

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Sébastien Gouëzel. "Almost sure invariance principle for dynamical systems by spectral methods." Ann. Probab. 38 (4) 1639 - 1671, July 2010. https://doi.org/10.1214/10-AOP525

Information

Published: July 2010
First available in Project Euclid: 8 July 2010

zbMATH: 1207.60026
MathSciNet: MR2663640
Digital Object Identifier: 10.1214/10-AOP525

Subjects:
Primary: 37C30, 60F17

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 4 • July 2010
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