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

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 semilin...

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Bibliographic Details
Published in:arXiv.org 2020-04
Main Authors: Bardina, Xavier, Juan Pablo Márquez, Quer-Sardanyons, Lluís
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Fields (mathematics)
Stochastic processes
Thermodynamics
White noise
Online Access:Get full text
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Summary: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.
ISSN:2331-8422