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 | , , |
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| Format | Journal Article |
| Language | English |
| Published |
18.07.2019
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| Subjects | |
| Online Access | Get full text |
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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 |
| Author_xml | – sequence: 1 givenname: Xavier surname: Bardina fullname: Bardina, Xavier – sequence: 2 givenname: Juan Pablo surname: Márquez fullname: Márquez, Juan Pablo – sequence: 3 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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| SubjectTerms | Mathematics - Probability |
| Title | Weak approximation of the complex Brownian sheet from a L\'evy sheet and applications to SPDEs |
| URI | https://arxiv.org/abs/1907.08117 |
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