Symmetries and Functions of Markov Processes

Abstract

From the symmetries contained in the collection of excessive functions of a transient Hunt process $X(t)$ on a state space $E$, we construct a quotient space $F$, a function $\Phi: E \rightarrow F$ and a time change $\tau(t)$ of $X(t)$ so that $\Phi(X(\tau_t))$ is a strong Markov process.