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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:479

Article

Slaoui, Meryem¹  Tudor, Ciprian A.^1,2 

[1] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

[2] Romanian Acad, ISMMA, Bucharest, Romania

关键词: Wiener chaos, Hermite process;    Stochastic heat equation;    Fractional Brownian motion;    Multiple stochastic integrals;    Malliavin calculus;   

DOI  :  10.1016/j.jmaa.2019.06.031

来源: Elsevier

【 摘 要 】

We consider the Wiener integral with respect to a d-parameter Hermite process with Hurst multi-index H = (H-1, .., H-d) is an element of (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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free