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Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs (1907.08117v2)
Published 18 Jul 2019 in math.PR
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.
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