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2010, Volume 14, Issue 2: 473-493. Doi: 10.3934/dcdsb.2010.14.473
This issue Previous Article Escape rates and Perron-Frobenius operators: Open and closed dynamical systems Next Article Zero, one and two-switch models of gene regulation

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

  • 1.

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

  • 2.

    346 TMCB Brigham Young University, Provo, UT 84602

  • 3.

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

Received:  April 30, 2009
Revised:  September 30, 2009
Published:  August 2010
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: Primary: 37L55; Secondary: 60H15, 37L25, 35R60, 58B99.

    Citation:
    shu

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