Existence and Uniqueness of Quasi-Stationary Distributions for Symmetric Markov Processes with Tightness Property

TL;DR

This paper proves the existence and uniqueness of quasi-stationary distributions for symmetric Markov processes that are explosive and possess a tightness property, expanding understanding of their long-term behavior.

Contribution

It establishes the conditions under which symmetric Markov processes with certain properties have unique quasi-stationary distributions, a novel result for explosive processes.

Findings

Existence of quasi-stationary distributions under specified conditions

Uniqueness of these distributions for the class of processes studied

Extension of quasi-stationary distribution theory to explosive symmetric Markov processes

Abstract

Let $X$ be an irreducible symmetric Markov process with the strong Feller property. We assume, in addition, that $X$ is explosive and has a tightness property. We then prove the existence and uniqueness of quasi-stationary distributions of $X$.