Almost sure central limit theorems on the Wiener space

TL;DR

This paper establishes almost sure central limit theorems for sequences of Gaussian functionals, including non-linear functions of stationary Gaussian sequences, demonstrating convergence to normal distribution.

Contribution

It extends almost sure CLTs to general Gaussian fields and non-linear functions, providing new convergence results in this context.

Findings

Almost sure CLTs hold for non-linear functions of stationary Gaussian sequences.

Results apply to general Gaussian fields.

Convergence to normal distribution is established under specified conditions.

Abstract

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution.