Convergence and representation theorems for set valued random processes

Abstract

In this paper we study set valued random processes in discrete time and with values in a separable Banach space. We start with set valued martingales and prove various convergence and regularity results. Then we turn our attention to larger classes of set valued processes. So we introduce and study set valued amarts and set valued martingales in the limit. Finally we prove a useful property of the set valued conditional expectation