Title :

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

Author(s) :

Slaoui, Meryem [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Tudor, Ciprian A. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Mathematical Analysis and Applications

Publisher :

Elsevier

Publication date :

2019-06

ISSN :

0022-247X

English keyword(s) :

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

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL