Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Abstract

Using recent results on the behavior of multiple Wiener-It\^o integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.Comment: To appear in "Electronic Communications in Probability