Time Reversal on Levy Processes

Abstract

Time reversal of semimartingales defined on a Levy process framework is considered. Usually semimartingales cannot be time-reversed such that the reversed process is still a semimartingale. An expansion-of-filtrations result for Levy processes is established and then it is used to give sufficient conditions such that a semimartingale defined on a Levy process can be time-reversed and still remain a semimartingale.