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ON THE LONGEST RUNS IN MARKOV CHAINS
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.
2018 (English)In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 38, no 2, p. 407-428Article in journal (Refereed) Published
Abstract [en]

In the first n steps of a two-state (success and failure) Markov chain, the longest success run L(n) has been attracting considerable attention due to its various applications. In this paper, we study L(n) in terms of its two closely connected properties: moment generating function and large deviations. This study generalizes several existing results in the literature, and also finds an application in statistical inference. Our method on the moment generating function is based on a global estimate of the cumulative distribution function of L(n) proposed in this paper, and the proofs of the large deviations include the Gartner-Ellis theorem and the moment generating function.

Place, publisher, year, edition, pages
WYDAWNICTWO UNIWERSYTETU WROCLAWSKIEGO , 2018. Vol. 38, no 2, p. 407-428
Keywords [en]
Longest run; moment generating function; large deviation principle; Markov chain
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-154770DOI: 10.19195/0208-4147.38.2.8ISI: 000456711200008OAI: oai:DiVA.org:liu-154770DiVA, id: diva2:1291702
Available from: 2019-02-26 Created: 2019-02-26 Last updated: 2019-02-26

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