Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion
The authors study nonlinear stochastic partial differential equations (SPDEs) driven by a fractional Brownian motion (fBm) with the Hurst parameter bigger than 1/2. They prove 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, they emphasize that the coefficients in front of the fractional noise are non-trivial. The obtained results can be applied to many concrete random dynamical systems generates from stochastic mathematical physics equations driven by a fractional Brownian motion.
scientific article; zbMATH DE number 5790143