Strong invariance principles with rate for "reverse" martingales and applications

Abstract

In this paper, we obtain almost sure invariance principles with rate of order $n^{1/p}{\log }^{\beta }n$, $2<p\le 4$, for sums associated to a sequence of reverse martingale differences. Then, we apply those results to obtain similar conclusions in the context of some non-invertible dynamical systems. For instance we treat several classes of uniformly expanding maps of the interval (for possibly unbounded functions). A general result for $\varphi$-dependent sequences is obtained in the course.

29 pages

References in corpus (1)

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

Cited by in corpus (1)

• Law of the iterated logarithm for the periodogram