Approximate Controllability Result for Backward Stochastic Evolution Inclusions in Hilbert Spaces

Abstract

In this paper, we study semilinear backward stochastic evolution inclusion systems in Hilbert spaces. First, we prove the existence of mild solution of the semilinear backward stochastic evolution inclusion systems using a multivalued fixed point theorem. Then, we obtain the approximate controllability result for semilinear backward stochastic evolution inclusion systems through the linear systems corresponding to these semilinear backward stochastic evolution inclusion systems under appropriate conditions. In particular, our study extends the results of the concept of approximate controllability to backward sto- chastic evolution inclusion systems.