Viability for impulsive stochastic differential inclusions driven by fractional Brownian motion

Abstract

In this paper, we prove necessary and sufficient conditions for the viability for an impulsive stochastic functional differential inclusion driven by a fractional Brownian motion. The viable property is of interest since it reflects the stability of the model under consideration. The fractional Brownian motion provides a memory effect to the model. Whereas, the appearance of the impulsive factor introduces jumps to the solutions and is new to the analysis of this type. Hence our results are new even in the special case of stochastic differential equation setting.