  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.

Probability