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

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.