TITLE:
Set-Valued Stochastic Integrals with Respect to Finite Variation Processes
AUTHORS:
Jinping Zhang, Jiajia Qi
KEYWORDS:
Set-Valued Stochastic Process; Finite Variation Process; Measurability
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.9A,
December
18,
2013
ABSTRACT: In a Euclidean space Rd, 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 L2-bounded.