Raw time changes of Markov processes

Abstract

Let $A_t$ be a nonadapted continuous additive functional of a right continuous strong Markov process $X_t$, and let $\tau_t$ denote the right continuous inverse of $A_t$. We give general sufficient conditions for the time-changed process $X_{\tau_t}$ to again be a strong Markov process with a new transition semigroup. We give several examples and show that birthing a process at a last exit time and killing a process at a cooptional time may be realized as raw time changes.