A deviation inequality and quasi-ergodicity for absorbing Markov processes

Abstract

In this note, we study quasi-ergodic behavior for killed Markov process. For symmetric stable processes, we derive a conditional deviation inequality for \(\int _0^tV(X_s)\hbox {d}s\) for certain (unbounded) functions V. Then we apply it to prove a quasi \(L^1\)-ergodic theorem for the killed process.