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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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. |
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DOI: | 10.48550/arxiv.1907.08117 |