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

12 Jul 2019  ·  Slaoui Meryem LPP, Tudor Ciprian A. LPP ·

We consider the Wiener integral with respect to a $d$-parameter Hermite process with Hurst multi-index ${\bf H}= (H_{1},\ldots, H_{d}) \in \left( \frac{1}{2}, 1\right) ^{d}$ and we analyze the limit behavior in distribution of this object when the components of ${\bf H}$ 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...

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Probability