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arXiv · 1907.05633

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

Meryem Slaoui·Ciprian A. Tudor
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Abstract

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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Meryem Slaoui, Ciprian A. Tudor. 2019-07-12. Behavior with respect to the Hurst index of the Wiener Hermite integrals and application to SPDEs. https://doi.org/10.1016/j.jmaa.2019.06.031

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