Random dynamical systems for stochastic partial differential
equations driven by a fractional Brownian motion
María J. Garrido–Atienza - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain (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
Received: May 2009; Revised: October 2009; Published: June 2010.
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