Vector-valued stochastic processes. I. Vector measures and vector-valued stochastic processes with finite variation

Abstract

In this paper we study the relationshipμ V (M)=E(∫1 M dV S ) between operatorvalued processesV with finite variation ⋎V⋎ and operator-valued stochastic measuresμ V with finite variation |μ V |. The variations satisfy the inequality |μ V |⩽μ|V|, which, under certain conditions, is an equality (for example, ifV is measurable).