Green Measures for Time Changed Markov Processes

TL;DR

This paper investigates Green measures for time-changed Markov processes using inverse subordinators, establishing their existence and relation to original processes, with applications to fractional dynamics.

Contribution

It introduces conditions under which Green measures for inverse subordinated Markov processes exist and coincide with those of the original processes.

Findings

Green measures exist for certain time-changed Markov processes.

Green measures for the time-changed processes coincide with those of the original processes.

Applications to fractional dynamics are demonstrated.

Abstract

In this paper we study Green measures for certain classes of random time change Markov processes where the random time change are inverse subordinators. We show the existence of the Green measure for these processes under the condition of the existence of the Green measure of the original Markov processes and they coincide. Applications to fractional dynamics in given.