Concepts of Dichotomy for Stochastic Skew-Evolution Semiflows in Hilbert Spaces

The paper presents some exponential dichotomy concepts in mean square for stochastic skew-evolution semiflows generated by stochastic differential equations in Hilbert spaces. The obtained results are generalizations for the stochastic case of some well-known theorems about uniform exponential dichotomy of variational systems in the deterministic case. Finally, we present some open problems and motivate their connections with previous results in this topic.