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

Meryem Slaoui (1) , Ciprian A. Tudor (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

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.

Mots clés: Wiener chaos; Hermite process; stochastic heat equa- tion; fractional Brownian motion; multiple stochastic integrals; Malliavin calculus; Fourth Moment Theorem; multiparameter stochastic processes

Domaines: Probabilités [math.PR]

Meryem Slaoui, Ciprian A. Tudor. Behavior with respect to the Hurst index of the Wiener Hermite integrals and application to SPDEs. Journal of Mathematical Analysis and Applications, 2019, ⟨10.1016/j.jmaa.2019.06.031⟩. ⟨hal-02181051⟩