Pointwise ergodic theorems with rate and application to limit theorems for stationary processes

By C. Cuny. 2009

51 citations recorded by the source corpus.

We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving $\|\sum_{k=1} ^nf\circ \theta^k\|_2$, improving previous results. Then, using known results on martingale approximation, we obtain some LIL for stationary ergodic processes and quenched central limit theorems for functional of Markov chains. 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.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6c7d8cf36272a1c178244ada9bf3f436f2610da0

Citations in the corpus

• Central limit theorem for Markov processes with spectral gap in the Wasserstein metric (2011, unknown): “[2, 4, 5, 10].”