Random attractors and invariant measures for semilinear stochastic FDEEs with infinite delay in Hilbert space
Xiaohui Wang, Xianlong Fu
Source abstract
This paper studies the existence of random attractors and invariant measures of a semilinear stochastic functional differential evolution equation with infinite delay in Hilbert space driven by Q-Wiener processes. We first investigate the existence and uniqueness of solutions as well as the existence of a continuous non-autonomous random dynamical system for the considered equation. Then, by employing techniques concerning Kuratowski’s measure of non-compactness and D-pullback asymptotic compactness, the existence of tempered D-pullback random attractors is proved. Following this, the existence and uniqueness of (periodic) invariant measures, which are supported on D-pullback random attractors, are established for the equation. Finally, an example is provided to demonstrate the obtained results.
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