Weak approximation of the complex Brownian sheet from a L\'evy sheet and applications to SPDEs

We consider a L\'evy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain weak approximations of the random field solution to a...

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Bibliographic Details
Main Authors Bardina, Xavier, Márquez, Juan Pablo, Quer-Sardanyons, Lluís
Format Journal Article
LanguageEnglish
Published 18.07.2019
Subjects
Mathematics - Probability
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Summary:We consider a L\'evy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain weak approximations of the random field solution to a semilinear one-dimensional stochastic heat equation driven by the space-time white noise.
DOI:10.48550/arxiv.1907.08117