Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion

Pages: 473 - 493, Volume 14, Issue 2, September 2010

doi:10.3934/dcdsb.2010.14.473       Abstract        Full Text (254.5K)       Related Articles

María J. Garrido–Atienza - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain (email)
Kening Lu - 346 TMCB Brigham Young University, Provo, UT 84602, United States (email)
Björn Schmalfuss - Institut für Mathematik, Fakultät EIM, Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany (email)

Abstract: In this paper we study nonlinear stochastic partial differential equations (SPDEs) driven by a fractional Brownian motion (fBm) with the Hurst parameter bigger than $1/2$. We show that these SPDEs generate random dynamical systems (or stochastic flows) by using the stochastic calculus for an fBm where the stochastic integrals are defined by integrands given by fractional derivatives. In particular, we emphasize that the coefficients in front of the fractional noise are non-trivial.

Keywords:  Stochastic PDEs, fractional Brownian motion, random dynamical systems.
Mathematics Subject Classification:  Primary: 37L55; Secondary: 60H15, 37L25, 35R60, 58B99.

Received: May 2009;      Revised: October 2009;      Published: June 2010.