Dynamics of SPDEs driven by a small fractional brownian motion with hurst parameter larger than 1/2

Abstract

We consider mild solutions of an SPDE driven by a time dependent perturbation which is Hölder continuous with a Hölder exponent larger than 1/2. In particular, such a perturbation is given by a fractional Brownian motion with Hurst parameter larger than 1/2. The coefficient in front of this noise is an operator with bounded first and second derivatives. We formulate conditions such that the equation has a unique pathwise solution. Further we investigate the globally exponential stability of the trivial solution.