Weak convergence to the fractional Brownian sheet from a Lévy sheet

2020/02/14 by Bardina, Xavier, Rovira, Carles
#60F05 #60G15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2002.06263

Abstract

In this paper, we show an approximation in law, in the space of the continuous functions on [0,1]², of two-parameter Gaussian processes that can be represented as a Wiener type integral by processes constructed from processes that converge to the Brownian sheet. As an application, we obtain a sequence of processes constructed from a Lévy sheet that converges in law towards the fractional Brownian sheet.

Related

• Weak approximation for Gaussian processes from renewal processes
• Weak convergence towards two independent Gaussian processes from a unique Poisson process
• Convergence to Weighted Fractional Brownian Sheets
• Convergence of finite-dimensional laws of the weighted quadratic variations process for some fractional Brownian sheets
• Decomposition and limit theorems for a class of self-similar Gaussian processes