Stochastic shell models driven by a multiplicative fractional Brownian-motion

PHYSICA D-NONLINEAR PHENOMENA

卷:320

Article

Bessaih, Hakima¹  Garrido-Atienza, Maria J.²  Schmalfuss, Bjorn³ 

[1] Univ Wyoming, Dept Math, Laramie, WY 82071 USA

[2] Univ Seville, Dpto Ecuac Diferenciales & Anal Numer, Apdo Correos 1160, Seville 41080, Spain

[3] Univ Jena, Inst Stochast, Ernst Abbe Pl 2, D-77043 Jena, Germany

关键词: Stochastic PDEs;    Fractional Brownian-motion;    Pathwise solutions;    Fractional calculus;   

DOI  :  10.1016/j.physd.2016.01.008

来源: Elsevier

【 摘 要 】

We prove existence and uniqueness of the solution of a stochastic shell-model. The equation is driven by an infinite dimensional fractional Brownian-motion with Hurst-parameter H is an element of (1/2, 1), and contains a non-trivial coefficient in front of the noise which satisfies special regularity conditions. The appearing stochastic integrals are defined in a fractional sense. First, we prove the existence and uniqueness of variational solutions to approximating equations driven by piecewise linear continuous noise, for which we are able to derive important uniform estimates in some functional spaces. Then, thanks to a compactness argument and these estimates, we prove that these variational solutions converge to a limit solution, which turns out to be the unique pathwise mild solution associated to the shell-model with fractional noise as driving process. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free