Behavior with respect to the Hurst index of the Wiener Hermite integrals and application to SPDEs

Abstract

We consider the Wiener integral with respect to a $d$-parameter Hermite process with Hurst multi-index $\mathbf{H}=(H_1,\dots ,H_d)\in {\left(\frac{1}{2},1\right)}^d$ and we analyze the limit behavior in distribution of this object when the components of $\mathbf{H}$ tend to $1$ and/or $\frac{1}{2}$. As examples, we focus on the solution to the stochastic heat equation with additive Hermite noise and to the Hermite Ornstein-Uhlenbeck process.

Journal of Mathematical Analysis and Applications, Elsevier, 2019

References in corpus (2)

• Central limit theorems for sequences of multiple stochastic integrals
• Wiener integrals with respect to the Hermite random field and applications to the wave equation