Hostname: page-component-7dd5485656-wlg5v Total loading time: 0 Render date: 2025-10-30T11:07:38.907Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Embedding Certain Bernoulli Sequences in Marked Poisson Processes

Part of: Special processes Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Lars Holst
Lars Holst*
Affiliation:
Royal Institute of Technology
*
∗ Postal address: Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden. Email address: lholst@math.kth.se
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A sequence of independent Bernoulli random variables with success probabilities a / (a + b + k − 1), k = 1, 2, 3, …, is embedded in a marked Poisson process with intensity 1. Using this, conditional Poisson limits follow for counts of failure strings.

Keywords

Bernoulli trialconditional limit theoremPoisson limitrandom permutationrecordsums of indicators

MSC classification

Secondary: 60C05: Combinatorial probability 60K99: None of the above, but in this section

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 1181 - 1185
Copyright
Copyright © Applied Probability Trust 2008 

References

Arratia, R., Barbour, A. D. and Tavaré, S. (2003). Logarithmic Combinatorial Structures: A Probabilistic Approach. European Mathematical Society, Zürich.CrossRefGoogle Scholar
Holst, L. (2007). Counts of failure strings in certain Bernoulli sequences. J. Appl. Prob. 44, 824–830.CrossRefGoogle Scholar
Holst, L. (2008). The number of two consecutive successes in a Hoppe–Pólya urn. J. Appl. Prob. 45, 901–906.CrossRefGoogle Scholar
Huffer, F., Sethuraman, J. and Sethuraman, S. (2008). A study of counts of Bernoulli strings via conditional Poisson processes. To appear in Proc. Amer. Math. Soc. Google Scholar
Kingman, J. F. C. (1993). Poisson Processes (Oxford Studies Prob. 3). Oxford University Press.Google Scholar