Year: 2022
Type: preprint
Abstract: In this paper, we study the stochastic heat equation (SHE) on $\mathbb{R}^d$ subject to a centered Gaussian noise that is white in time and colored in space. We establish the existence and uniqueness of the random field solution in the presence of locally Lipschitz drift and diffusion coefficients, which can have certain superlinear growth. This is a nontrivial extension of the recent work by Dalang, Khoshnevisan and Zhang (2019), where the one-dimensional SHE on $[0,1]$ subject to space-time white noise has been studied.
Source: arXiv (Cornell University)
Authors: Chen, Le, Huang, Jingyu
Institutions: Auburn University, University of Birmingham
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4302767325