The linear stochastic heat equation with Hermite noise

Abstract

We analyze the solution to the linear stochastic heat equation driven by a multiparameter Hermite process of order [Formula: see text]. This solution is an element of the [Formula: see text]th Wiener chaos. We discuss various properties of the solution, such as the necessary and sufficient condition for its existence, self-similarity, [Formula: see text]-variation and regularity of its sample paths. We will also focus on the probability distribution of the solution, which is non-Gaussian when [Formula: see text].