Set-valued stochastic integrals with respect to a real valued martingale

Abstract

In a real separable martingale type 2 Banach space, first we give the definition of single valued stochastic integrals by the differential of a real valued continuous L2-martingale, and then, consider the set-valued case. Submartingale property and Castaing representation of set-valued stochastic integrals are obtained. © 2008 Springer-Verlag Berlin Heidelberg.