Weak convergence to the fractional Brownian sheet from a L\'evy sheet

Xavier Bardina; Carles Rovira

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arXiv · 2002.06263

Weak convergence to the fractional Brownian sheet from a L\'evy sheet

Xavier Bardina·Carles Rovira

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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 L\'evy sheet that converges in law towards the fractional Brownian sheet.

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Xavier Bardina, Carles Rovira. 2020-02-14. Weak convergence to the fractional Brownian sheet from a L\'evy sheet. https://arxiv.org/abs/2002.06263

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