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Almost sure invariance principle for dynamical systems by spectral methods. (English) Zbl 1207.60026

Author’s abstract: We prove the almost sure invariance principle for stationary \(\mathbb R^d\)-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.

MSC:

60F17 Functional limit theorems; invariance principles
37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.
60G10 Stationary stochastic processes
60F15 Strong limit theorems
60J05 Discrete-time Markov processes on general state spaces
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