Dual spaces of cadlag processes

Abstract

This article characterizes topological duals of spaces of cadlag processes. We obtain extensions of functional analytic results of Dellacherie and Meyer that underlie many fundamental results in stochastic analysis. In particular, we obtain a characterization of the dual of cadlag processes of class $(D)$ in terms of optional measures of essentially bounded variation. When specialized to regular processes, we find extensions of the main result of Bismut \cite{bis78} on projections of continuous processes. The dual characterizations yield existence results and optimality conditions for many fundamental problems from optimal stopping to singular stochastic control well beyond classical formulations.