A study of counts of bernoulli strings via conditional poisson processes

Fred W. Huffer, Jayaram Sethuraman, Sunder Sethuraman

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

A sequence of random variables, each taking values 0 or 1, is called a Bernoulli sequence. We 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 paper, 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. In particular, this general class includes all Bernoulli sequences considered in the literature, as well as a host of new sequences.

Original languageEnglish (US)
Pages (from-to)2125-2134
Number of pages10
JournalProceedings of the American Mathematical Society
Volume137
Issue number6
DOIs
StatePublished - Jun 1 2009
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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