On a dyadic approximation of predictable processes of finite variation

Abstract

We show that any cadlag predictable process of finite variation is an a.s. limit of elementary predictable processes; it follows that predictable stopping times can be approximated `from below' by predictable stopping times which take finitely many values. We then obtain as corollaries two classical theorems: predictable stopping times are announceable, and an increasing process is predictable iff it is natural.Comment: version 5: To make the paper more readable I made the paper more self contained, and I have changed the order with which theorems are stated and prove