On the quasi-ergodic distribution of absorbing Markov processes

Abstract

In this paper, we give a sufficient condition for the existence of a quasi-ergodic distribution for absorbing Markov processes. Using an orthogonal-polynomial approach, we prove that the previous main result is valid for the birth-death process on the nonnegative integers with 0 an absorbing boundary and $\infty$ an entrance boundary. We also show that the quasi-ergodic distribution is stochastically larger than the unique quasi-stationary distribution in the sense of monotone likelihood-ratio ordering for the birth-death process.

This paper is published in Statistics & Probability Letters (2019)

References in corpus (1)

• On quasi-ergodic distribution for one-dimensional diffusions

Cited by in corpus (1)

• Dynamics of continuous time Markov chains with applications