H\"older estimates and weak convergences of certain weighted sum processes

TL;DR

This paper establishes H"older continuity and weak convergence results for weighted sum processes in Wiener chaos, utilizing Malliavin calculus, the fourth moment theorem, and Young integral estimates.

Contribution

It introduces new H"older estimates and a functional limit theorem for weighted sum processes in Wiener chaos, advancing the understanding of their convergence properties.

Findings

Proved H"older estimates for weighted sum processes.

Established a functional limit theorem for these processes.

Applied Malliavin calculus and Young integrals in the analysis.

Abstract

We study weighted sum processes associated to elements in a Wiener chaos with fixed order. More precisely, we show H\"older estimates and a functional limit theorem for them. Main tools we use are the integration by parts formula in Malliavin calculus, the fourth moment theorem, and estimates in multidimensional Young integrals.