Set-Valued Stochastic Integrals with Respect to Finite Variation Processes

Abstract

In a Euclidean space R d , the Lebesgue-Stieltjes integral of set-valued stochastic processes with respect to real valued finite variation process is defined directly by employing all integrably bounded selections instead of taking the decomposable closure appearing in some existed references. We shall show that this kind of integral is measurable, continuous in t under the Hausdorff metric and L 2 -bounded.