On measurable multifunctions with stochastic domain

Abstract

AbstractIn this paper we prove several random fixed point theorems for multifunctions with a stochastic domain. Then those techniques are used to establish the existence of solutions for random differential inclusions. A useful tool in this process is a stochastic version of the Tietze extension theorems that we prove. Finally we present a stochastic version of the Riesz representation theorem for Hilbert spaces.