Almost sure limit theorems on Wiener chaos: the non-central case

2018/07/23 by Azmoodeh, Ehsan, Nourdin, Ivan
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1807.08642

Abstract

In \citeBNT, a framework to prove almost sure central limit theorems for sequences (G_n) belonging to the Wiener space was developed, with a particular emphasis of the case where G_n takes the form of a multiple Wiener-Itô integral with respect to a given isonormal Gaussian process. In the present paper, we complement the study initiated in \citeBNT, by considering the more general situation where the sequence (G_n) may not need to converge to a Gaussian distribution. As an application, we prove that partial sums of Hermite polynomials of increments of fractional Brownian motion satisfy an almost sure limit theorem in the long-range dependence case, a problem left open in \citeBNT.

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