Stochastic GE-evolution operator method for controllability of time varying stochastic degenerate Sobolev equations in Banach spaces

This paper discusses exact and approximate controllability and exact and approx- imate observability of time varying stochastic degenerate Sobolev equations by stochastic GE-evolution operator method in Banach spaces. Firstly, we discuss exis- tence and uniqueness of the mild solution to time varying stochastic degenerate Sobolev equations by stochastic GE-evolution operator in Banach space. Secondly, we discuss conditions for exact and approximate controllability and exact and approximate observability of the stochastic degenerate Sobolev equations consid- ered in terms of stochastic GE-evolution operator and the dual principle. Finally, an illustrative example is given.