Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs

Xavier Bardina, Juan Pablo Márquez and Lluís Quer-Sardanyons

Stochastic Processes and their Applications, 2020, vol. 130, issue 9, 5735-5767

Abstract: We consider a Lévy 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.

Keywords: Brownian sheet; Lévy sheet; Stochastic heat equation; Weak approximation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:9:p:5735-5767

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DOI: 10.1016/j.spa.2020.04.006

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