A study of counts of Bernoulli strings via conditional Poisson processes

dc.creatorHuffer, Fred W.
dc.creatorSethuraman, Jayaram
dc.creatorSethuraman, Sunder
dc.date2008-01-14
dc.date.accessioned2026-07-07T08:54:21Z
dc.date.available2026-07-07T08:54:21Z
dc.descriptionWe say that a string of length $d$ occurs, in a Bernoulli sequence, if a success is followed by exactly $(d-1)$ failures before the next success. The counts of such $d$-strings are of interest, and in specific independent Bernoulli sequences are known to correspond to asymptotic $d$-cycle counts in random permutations. In this note, we give a new framework, in terms of conditional Poisson processes, which allows for a quick characterization of the joint distribution of the counts of all $d$-strings, in a general class of Bernoulli sequences, as certain mixtures of the product of Poisson measures. This general class includes all Bernoulli sequences considered before, as well many new sequences.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0801.2115
dc.identifierhttp://arxiv.org/abs/0801.2115
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145904
dc.subjectProbability
dc.subject60C05; 60K99
dc.titleA study of counts of Bernoulli strings via conditional Poisson processes
dc.typetext

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