Abstract
We consider the number of overlappingoccurrences up to a fixed time of one or several “rare ”patterns in a stationary finite-state Markov chain. We derive a bound for the total variation distance between the distribution of this quantity and a compound Poisson distribution, using general results on compound Poisson approximation for Markov chains by Erhardsson. If the state space is
Citation
Torkel Erhardsson. "Compound Poisson approximation for counts of rare patterns in Markov chains and extreme sojourns in birth-death chains." Ann. Appl. Probab. 10 (2) 573 - 591, May 2000. https://doi.org/10.1214/aoap/1019487356
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