Abstract

We consider the Wiener integral with respect to a d-parameter Hermite process with Hurst multi-index H=(H1,..,Hd)∈(12,1)d and we analyze the limit behavior in distribution of this object when the components of H tend to 1 and/or 12. As examples, we focus on the solution to the stochastic heat equation with additive Hermite noise and to the Hermite Ornstein-Uhlenbeck process.

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