Often in applications (for example Survival Analysis and Credit Risk) one begins with a totally inaccessible stopping time, and then one assumes the compensator has absolutely continuous paths. This gives an interpretation in terms of a ``hazard function'' process. Ethier and Kurtz have given sufficient conditions for a given stopping

time to have an absolutely continuous compensator, and this condition was extended by Yan Zeng to a necessary and sufficient condition. We take a different approach and make a simple hypothesis on the filtration under which all totally inaccessible stopping times have absolutely continuous compensators. We show such a property is stable under changes of measure, and under the expansion of filtrations; and we detail its limited stability under filtration shrinkage. The talk is based on research performed with Sokhna M'Baye and Svante Janson.