Compound Poisson approximation for counts of rare patterns in Markov chains and extreme sojourns in birth-death chains.

DOI10.1214/aoap/1019487356zbMath1063.60007OpenAlexW2035927204MaRDI QIDQ1884831

Torkel Erhardsson

Publication date: 27 October 2004

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1019487356

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Central limit and other weak theorems (60F05) Combinatorial probability (60C05) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (10)

Compound Poisson approximation ⋮ Strong memoryless times and rare events in Markov renewal point processes. ⋮ Some results associated with the longest run in a strongly ergodic Markov chain ⋮ Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source ⋮ Distribution of patterns of constrained length in binary sequences ⋮ On exceedances of high levels ⋮ Approximation for counts of head runs ⋮ On the First k Moments of the Random Count of a Pattern in a Multistate Sequence Generated by a Markov Source ⋮ A Compound Poisson Approximation Inequality ⋮ Stein's method for conditional compound Poisson approximation

Cites Work

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• High-Level exceedances of regenerative and semi-stationary processes
• Limit theorems for the number of occurrences of consecutive k successes in n Markovian trials
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