# Weak approximation of the complex Brownian sheet from a L\'evy sheet and applications to SPDEs

## TL;DR

This paper constructs a family of complex-valued random fields from a planar Lévy process that converge to a complex Brownian sheet, enabling weak approximation of solutions to certain stochastic partial differential equations.

## Contribution

It introduces a novel approximation method for the complex Brownian sheet using Lévy processes and applies it to approximate solutions of stochastic heat equations.

## Key findings

- Convergence of Lévy-based fields to the complex Brownian sheet
- Weak approximation of stochastic heat equation solutions
- Application to SPDEs driven by space-time white noise

## 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.