A central limit theorem for continuous-time Markov processes conditioned not to be absorbed

TL;DR

This paper proves a central limit theorem for continuous-time Markov processes conditioned on survival, extending understanding of their long-term behavior under general quasi-stationary conditions.

Contribution

It introduces a general framework for a central limit theorem for Markov processes conditioned on non-absorption, utilizing the $Q$-process and ergodic properties.

Findings

Established a CLT for ergodic Markov processes.

Derived a conditional CLT for processes conditioned not to be absorbed.

Provides a theoretical foundation for analyzing conditioned Markov processes.

Abstract

This paper aims to establish a central limit theorem for Markov processes conditioned not to be absorbed under a very general assumption on quasi-stationarity for the underlying process. To do so, a central limit theorem has been established for ergodic Markov processes. The conditional central limit theorem is then obtained by applying the central limit theorem to the $Q$-process.