Weak approximation of the complex Brownian sheet from a L\'evy sheet and applications to SPDEs
Probability
2020-04-28 v2
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.
Keywords
Cite
@article{arxiv.1907.08117,
title = {Weak approximation of the complex Brownian sheet from a L\'evy sheet and applications to SPDEs},
author = {Xavier Bardina and Juan Pablo Márquez and Lluís Quer-Sardanyons},
journal= {arXiv preprint arXiv:1907.08117},
year = {2020}
}
Comments
Final accepted version after a major revision