Limit theorems for functionals of Gaussian vectors

TL;DR

This paper establishes limit theorems for functionals of Gaussian vectors, showing that under certain conditions, their partial sums converge to an operator self-similar process, extending the understanding of Gaussian process behavior.

Contribution

It introduces new limit theorems for functionals of Gaussian vectors, generalizing previous results to operator self-similar processes.

Findings

Partial sums of Gaussian vector functionals converge to operator self-similar processes

Conditions identified for convergence to operator self-similar limits

Extends classical limit theorems to multivariate Gaussian settings

Abstract

Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process