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.
Categories: math.PR