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Inequalities for rare events in time-reversible Markov chains. II. (English) Zbl 0812.60054

Summary: A previous paper of the authors [part I, in: Inequalities in probability and statistics (Hayward, CA, 1992)] discussed explicit bounds in the exponential approximation for the distribution of the waiting time until a stationary reversible Markov chain first enters a ‘rare’ subset of states. In this paper Stein’s method is used to get explicit (but complicated) bounds on the Poisson approximation for the number of non- adjacent visits to a rare subset.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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References:

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[2] Aldous, D. J.; Brown, M., Inequalities for rare events in time-reversible Markov chains I, (Inequalities in Probability and Statistics (1992), IMS: IMS Hayward, CA) · Zbl 0812.60054
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