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.

This paper discusses exact and approximate controllability and exact and approximate observability of time varying stochastic implicit systems by GE-evolution operator method in Banach spaces. Firstly, we discuss existence and uniqueness of the mild solution to time varying stochastic implicit systems by stochastic GE-evolution operator in Banach space. Secondly, we discuss conditions for exact and approximate controllability and exact and approximate observability of the systems considered in terms of stochastic GE-evolution operator and the dual principle. Finally, an illustrative example is given.