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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: [email protected]
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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

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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
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