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

Xavier Bardina Simorra, Carles Rovira Escofet


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.


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

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ISSN: 1331-0623 (Print), 1848-8013 (Online)