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

Xavier Bardina Simorra; Carles Rovira Escofet

Vol. 26 No. 2 (2021)

Regular Articles

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

Published 2021-07-19

Xavier Bardina Simorra
Carles Rovira Escofet

Xavier Bardina Simorra
Universitat Autònoma de Barcelona

Carles Rovira Escofet
Universitat de Barcelona

Submission of an original manuscript to the Mathematical Communications will be taken to mean that it represents original work not previously published, that it is not being considered elsewhere for publication; and, if accepted for publication, it will be published in print and online form and it will not be published elsewhere in the same form, for commercial purposes, in any language, without the consent of the publisher. The journal takes the stance that the publication of scholarly research is meant to disseminate knowledge and, in a not-for-profit regime, benefits neither publisher nor author financially. It sees itself as having an obligation to its authors and to society to make content available online now that the technology allows for such a possibility.

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

PDF

Supplementary File(s)

TeX