A multiple stochastic integral criterion for almost sure limit theorems

Abstract

In this paper, we study almost sure entral limit theorems for multiple stohasti integrals and provide a riterion based on the kernel of these multiple integrals. We apply our result to normalized partial sums of Hermite polynomials of inrements of frational Brownian motion. We obtain almost sure entral limit theorems for these normalized sums when they onverge in law to a normal distribution.