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A general large deviation principle for longest runs
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
2016 (English)In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 110, 128-132 p.Article in journal (Refereed) Published
Abstract [en]

In this note we prove a general large deviation principle (LDP) for the longest success run in a sequence of independent Bernoulli trails. This study not only recovers several recently derived LDPs, but also gives new LDPs for the longest success run. The method is based on the Bryc’s inverse Varadhan lemma, which can be intuitively generalized to the longest success run in a two-state (success and failure) Markov chain.

Place, publisher, year, edition, pages
2016. Vol. 110, 128-132 p.
Keyword [en]
Longest run; Large deviation principle; Bernoulli trail; Markov chain
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-126109DOI: 10.1016/j.spl.2015.12.015ISI: 000374627200016OAI: oai:DiVA.org:liu-126109DiVA: diva2:911843
Available from: 2016-03-14 Created: 2016-03-14 Last updated: 2016-05-19

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Liu, ZhenxiaYang, Xiangfeng
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