Viable solutions of lower semicontinuous quantum stochastic differential inclusions

Abstract

We establish the existence and some properties of viable solutions of lower semicontinuous quantum stochastic differential inclusions within the framework of the Hudson–Parthasarathy formulations of quantum stochastic calculus. The main results here are accomplished by establishing a major auxiliary selection result. The results here extend the classical Nagumo viability theorems,valid on finite dimensional Euclidean spaces, to the present infinite dimensional locally convex space of noncommutative stochastic processes.