Original scientific paper

Weak convergence to a class of two-parameter Gaussian processes from a Lévy sheet

Xavier Bardina Simorra orcid.org/0000-0003-1803-3401 ; Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain
Carles Rovira Escofet ; Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, Spain

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.

Keywords

fractional Brownian sheet; weak convergence; Lérant PGC2018-097848-B-I00 from MINECOvy sheet; two-parameter Gaussian processes

Hrčak ID:

261507

URI

https://hrcak.srce.hr/261507

Publication date:

26.8.2021.

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