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arXiv · 1707.08419

Quasi-stationarity and quasi-ergodicity for discrete-time Markov chains with absorbing boundaries moving periodically

William Oçafrain
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Abstract

We are interested in quasi-stationarity and quasi-ergodicity when the absorbing boundary is moving. First we show that, in the moving boundary case, the quasi-stationary distribution and the quasi-limiting distribution are not well-defined when the boundary is oscillating periodically. Then we show the existence of a quasi-ergodic distribution for any discrete-time irreducible Markov chain defined on a finite space state in the fixed boundary case. Finally we use this last result to show the quasi-ergodicity in the moving boundary case.

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William Oçafrain. 2017-07-26. Quasi-stationarity and quasi-ergodicity for discrete-time Markov chains with absorbing boundaries moving periodically. https://arxiv.org/abs/1707.08419

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