Convergence of finite-dimensional laws of the weighted quadratic variations process for some fractional Brownian sheets

TL;DR

This paper proves a central limit theorem for the finite-dimensional distributions of the quadratic variations of fractional Brownian sheets, using Malliavin calculus techniques.

Contribution

It introduces a new CLT for fractional Brownian sheets' quadratic variations, extending previous results to a broader class of stochastic processes.

Findings

Established a CLT for finite-dimensional laws of quadratic variations

Applied Malliavin calculus to fractional Brownian sheets

Extended understanding of stochastic process convergence

Abstract

In this paper we state and prove a central limit theorem for the finite-dimensional laws of the quadratic variations process of certain fractional Brownian sheets. The main tool of this article is a method developed by Nourdin and Nualart based on the Malliavin calculus.