Mean-square invariant manifolds for stochastic differential equations with jumps

This paper aims to investigate the mean-square invariant manifolds for a class of stochastic differential equations with jumps. We first prove the existence of mean-square random invariant unstable manifolds for mean-square random dynamical systems, which involves the filtration generated by both a Brownian motion and a Poisson random measure. Then, we establish the existence of mean-square random stable invariant sets.