POINTWISE ERGODIC THEOREMS WITH RATE WITH APPLICATIONS TO LIMIT THEOREMS FOR STATIONARY PROCESSES

Abstract

We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving [Formula: see text], improving previous results. Then, using known results on martingale approximation, we obtain conditions for the Law of the Iterated Logarithm and for the quenched central limit theorem. The proofs are based on the use of the spectral theorem and, on a recent work of Zhao–Woodroofe extending a method of Derriennic–Lin.