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September  2010, 14(2): 473-493. doi: 10.3934/dcdsb.2010.14.473

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

María J. Garrido–Atienza 1, , Kening Lu 2, and  Björn Schmalfuss 3,

1. 

Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain
2. 

346 TMCB Brigham Young University, Provo, UT 84602, United States
3. 

Institut für Mathematik, Fakultät EIM, Universität Paderborn, Warburger Strasse 100, 33098 Paderborn

Received  May 2009 Revised  October 2009 Published  June 2010

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: random dynamical systems., Stochastic PDEs, fractional Brownian motion.
Mathematics Subject Classification: Primary: 37L55; Secondary: 60H15, 37L25, 35R60, 58B9.
Citation: María J. Garrido–Atienza, Kening Lu, Björn Schmalfuss. Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 473-493. doi: 10.3934/dcdsb.2010.14.473
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