Time change, jumping measure and Feller measure

Abstract

In this paper, we shall investigate some potential theory for time change of Markov processes. Under weak duality, it is proved that the jumping measure and Feller measure are actually independent of time change, and the jumping measure of a time changed process induced by a PCAF supported on $V$ coincides with the sum of the Feller measure on $V$ and the trace of the original jumping measure on $V$.