Occupancy distributions in Markov chains via Doeblin's ergodicity coefficient

Details Occupancy distributions in Markov chains via Doeblin's ergodicity coefficient Occupancy distributions in Markov chains via Doeblin's ergodicity coefficient

2010-03-12

arxiv.org/abs/1003.2649v1

Mathematics

Probability

12 pages, 2 tables

Scientific paper

We apply Doeblin's ergodicity coefficient as a computational tool to approximate the occupancy distribution of a set of states in a homogeneous but possibly non-stationary finite Markov chain. Our approximation is based on new properties satisfied by this coefficient, which allow us to approximate a chain of duration n by independent and short-lived realizations of an auxiliary homogeneous Markov chain of duration of order ln(n). Our approximation may be particularly useful when exact calculations via first-step methods or transfer matrices are impractical, and asymptotic approximations may not be yet reliable. Our findings may find applications to pattern problems in Markovian and non-Markovian sequences that are treatable via embedding techniques.

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