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 H = (H 1 , .., H d ) ∈ 1 2 , 1 d and we analyze the limit behavior in distribution of this object when the components of H tend to 1 and/or 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.2010 AMS Classification Numbers: 60H05, 60H15, 60G22.