On the quasi-ergodic distribution of absorbing Markov processes

Guoman He; Hanjun Zhang; Yixia Zhu

doi:10.1016/j.spl.2019.02.001

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arXiv · 1611.01002

On the quasi-ergodic distribution of absorbing Markov processes

Guoman He·Hanjun Zhang·Yixia Zhu

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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.

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Guoman He, Hanjun Zhang, Yixia Zhu. 2016-11-03. On the quasi-ergodic distribution of absorbing Markov processes. https://doi.org/10.1016/j.spl.2019.02.001

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