In , 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 , 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 .
"Almost sure limit theorems on Wiener chaos: the non-central case." Electron. Commun. Probab. 24 1 - 12, 2019. https://doi.org/10.1214/19-ECP212