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arXiv · 1907.08117

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

Xavier Bardina·Juan Pablo Márquez·Lluís Quer-Sardanyons
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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.

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Xavier Bardina, Juan Pablo Márquez, Lluís Quer-Sardanyons. 2020-04-25. Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs. https://arxiv.org/abs/1907.08117

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