Quasi-Stationarity of Discrete-Time Markov Chains with Drift to Infinity

Pauline Coolen-Schrijner () and Phil Pollett ()
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Pauline Coolen-Schrijner: University of Durham, Science Laboratories
Phil Pollett: The University of Queensland

Methodology and Computing in Applied Probability, 1999, vol. 1, issue 1, 81-96

Abstract: Abstract We consider a discrete-time Markov chain on the non-negative integers with drift to infinity and study the limiting behavior of the state probabilities conditioned on not having left state 0 for the last time. Using a transformation, we obtain a dual Markov chain with an absorbing state such that absorption occurs with probability 1. We prove that the state probabilities of the original chain conditioned on not having left state 0 for the last time are equal to the state probabilities of its dual conditioned on non-absorption. This allows us to establish the simultaneous existence, and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasi-stationary distribution in the usual sense, a similar statement is not possible for the original chain.

Keywords: transient Markov chains; invariant measures; limiting conditional distributions; quasi-stationary distributions (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1010018406356

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