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Laplace Transform Asymptotics and Large Deviation Principles for Longest Success Runs in Bernoulli Trials
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden..
Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden..
2016 (engelsk)Inngår i: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, nr 3, s. 747-764Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

The longest stretch L(n) of consecutive heads in n independent and identically distributed coin tosses is seen from the prism of large deviations. We first establish precise asymptotics for the moment generating function of L(n) and then show that there are precisely two large deviation principles, one concerning the behavior of the distribution of L(n) near its nominal value log(1/p) n and one away from it. We discuss applications to inference and to logarithmic asymptotics of functionals of L(n).

sted, utgiver, år, opplag, sider
2016. Vol. 53, nr 3, s. 747-764
Emneord [en]
Large deviation principle, rate function, Fenchel-Legendre transform, Laplace transform, moment generating function, run, longest run, Bernoulli trial, confidence interval
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Identifikatorer
URN: urn:nbn:se:uu:diva-308783DOI: 10.1017/jpr.2016.38ISI: 000386349900008OAI: oai:DiVA.org:uu-308783DiVA, id: diva2:1053223
Forskningsfinansiär
Swedish Research CouncilTilgjengelig fra: 2016-12-08 Laget: 2016-11-30 Sist oppdatert: 2017-11-29bibliografisk kontrollert

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