Almost Sure Invariance Principles via Martingale Approximation
Probability
2011-05-05 v2
Abstract
In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale with stationary differences. The results are exploited to further investigate the central limit theorem and its invariance principle started at a point, as well as the law of the iterated logarithm via almost sure approximation with a Brownian motion, improving the results available in the literature. The conditions are well suited for a variety of examples; they are easy to verify, for instance, for linear processes and functions of Bernoulli shifts.
Cite
@article{arxiv.1103.6266,
title = {Almost Sure Invariance Principles via Martingale Approximation},
author = {Florence Merlevède and Costel Peligrad and Magda Peligrad},
journal= {arXiv preprint arXiv:1103.6266},
year = {2011}
}