Recurrence and Uniqueness Criteria for Markov Processes from Moments of Integral-Type Functionals

Abstract

We investigate recurrence and uniqueness of continuous-time Markov chains using moments of integral-type functionals. Unlike the classical criteria from Chen (2004) and the Feller-Reuter criterion, we develop general unified conditions for recurrence and uniqueness of Markov processes based on moments of integral-type functionals. The associated criteria follow directly from these conditions whenever the mean functionals can be expressed explicitly. As applications, explicit recurrence and uniqueness criteria are derived for single-birth, single-death, and birth-death processes on trees.