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A Note on Embedding Certain Bernoulli Sequences in Marked Poisson Processes

Part of: Combinatorial probability Special processes

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
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Abstract

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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
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