Almost Sure Invariance Principles via Martingale Approximation
arXiv:1103.6266
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.
References in corpus (4)
- Central limit theorem for Fourier transforms of stationary processes
- Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples
- Pointwise ergodic theorems with rate and application to limit theorems for stationary processes
- Central limit theorem started at a point for additive functionals of reversible Markov chains