# Yan Zeng

 Yan Zeng Ph.D. (2006) Cornell University

### First Position

Postdoctoral scholar at Florida State University

### Dissertation

Compensators of Stopping Times

Abstract: Let $(\Omega, ({\cal F}_t)_{t\ge 0}, {\cal F}, P)$ be a filtered probability space satisfying the usual hypotheses. Suppose $\tau$ is a stopping time and $N_t=1_{\{\tau\le t\}}$ is the associated point process. We consider when the Doob-Meyer decomposition of N has a compensator whose sample paths are a.s. absolutely continuous with respect to the Lebesgue measure. We prove a decomposition theorem which uniquely decomposes any totally inaccessible stopping time into two parts, such that one part has an absolutely continuous compensator and the other part has a singular compensator. We also characterize an absolutely continuous space, in which any totally inaccessible stopping time has an absolutely continuous compensator. A criterion of Ethier and Kurtz for the existence of an absolutely continuous compensator is extended, a corollary of which is that the absolute continuity of a compensator is preserved under filtration shrinkage.