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On Consecutive Records in Certain Bernoulli Sequences

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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In an infinite sequence of independent Bernoulli trials with success probabilities pk=a/(a+b +k-1) for k=1,2,3,…, let Nr be the number of r≥2 consecutive successes. Expressions for the first two moments of Nr are derived. Asymptotics of the probability of no occurrence of r consecutive successes for large r are obtained. Using an embedding in a marked Poisson process, it is indicated how the distribution of Nr can be calculated for small r.

Keywords

Bernoulli trialembedding in Poisson processrandom permutationrecordsruns of successessums 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 46 , Issue 4 , December 2009 , pp. 1201 - 1208
Copyright
Copyright © Applied Probability Trust 2009 

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