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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Main Authors Bardina, Xavier, Márquez, Juan Pablo, Quer-Sardanyons, Lluís
Format Journal Article
LanguageEnglish
Published 18.07.2019
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Abstract 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.
AbstractList 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.
Author Márquez, Juan Pablo
Quer-Sardanyons, Lluís
Bardina, Xavier
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  givenname: Lluís
  surname: Quer-Sardanyons
  fullname: Quer-Sardanyons, Lluís
BackLink https://doi.org/10.48550/arXiv.1907.08117$$DView paper in arXiv
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Snippet 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...
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Title Weak approximation of the complex Brownian sheet from a L\'evy sheet and applications to SPDEs
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