@article{d0f5a8d6f8d74012ae172e8c0fba99f2,
title = "Weak approximation of the complex Brownian sheet from a L{\'e}vy sheet and applications to SPDEs",
abstract = "We consider a L{\'e}vy 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 = "Brownian sheet, L{\'e}vy sheet, Stochastic heat equation, Weak approximation",
author = "Xavier Bardina and M{\'a}rquez, \{Juan Pablo\} and Llu{\'i}s Quer-Sardanyons",
note = "Funding Information: Research supported by the grant PGC2018-097848-B-I00 of the Ministerio de Econom{\'i}a y Competitividad, Spain . J.P. M{\'a}rquez was supported by a fellowship of CONACYT-M{\'e}xico . Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",
year = "2020",
month = sep,
language = "English",
volume = "130",
pages = "5735--5767",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",
number = "9",
}