Almost sure invariance principle for dynamical systems by spectral methods

Details Almost sure invariance principle for dynamical systems by spectral methods Almost sure invariance principle for dynamical systems by spectral methods

2009-07-08

arxiv.org/abs/0907.1404v3

Annals of Probability 38, 4 (2010) 1639-1671

Mathematics

Dynamical Systems

25 pages v2: minor revision v3: published version

Scientific paper

10.1214/10-AOP525

We prove the almost sure invariance principle for stationary R^d--valued
processes (with dimension-independent very precise error terms), solely under a
strong assumption on 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.

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