Absolutely Continuous Compensators

TL;DR

This paper establishes conditions under which all totally inaccessible stopping times in certain filtrations have absolutely continuous compensators, especially for semimartingale strong Markov processes represented via stochastic differential equations.

Contribution

It provides new sufficient conditions ensuring absolute continuity of compensators for totally inaccessible stopping times in semimartingale processes.

Findings

All totally inaccessible stopping times have absolutely continuous compensators under specified filtration conditions.

Semimartingale strong Markov processes can be represented by stochastic differential equations driven by Wiener, Lebesgue, and Poisson measures.

Compensators of such stopping times are absolutely continuous with respect to the minimal filtration generated by the process.

Abstract

We give sufficient conditions on the underlying filtration such that all totally inaccessible stopping times have compensators which are absolutely continuous. If a semimartingale, strong Markov process X has a representation as a solution of a stochastic differential equation driven by a Wiener process, Lebesgue measure, and a Poisson random measure, then all compensators of totally inaccessible stopping times are absolutely continuous with respect to the minimal filtration generated by X. However Cinlar and Jacod have shown that all semimartingale strong Markov processes, up to a change of time and space, have such a representation.