Theoretical analysis of a Stochastic Approximation approach for computing Quasi-Stationary distributions of general state space Markov chains

TL;DR

This paper extends a stochastic approximation algorithm to estimate quasi-stationary distributions from finite to general state space Markov chains, broadening its applicability under minimal assumptions.

Contribution

It provides a theoretical proof for a new algorithm that estimates quasi-stationary distributions in general state space Markov chains, generalizing previous finite state results.

Findings

Algorithm proven to work under broad conditions

Extends applicability to general state spaces

Provides theoretical guarantees for convergence

Abstract

An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general assumptions.