English

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