SPD

Abstract

First we prove existence and uniqueness for solutions of SPDE driven by an FBM ($H>1/2$) with nontrivial multiplicative noise in the space of H{\"o}lder continuous functions. Here $A$ is the negative generator of an analytic semigroup and $G$ satisfies regularity conditions. Later we use these solutions to generate a random dynamical system. This random dynamical system is smoothing and dissipative. These two properties then allow to conclude that this the SPDE has a random attractor.