On consecutive records in certain Bernoulli sequences
LARS HOLST
Source: J. Appl. Probab. Volume 46, Number 4
(2009), 1201-1208.
Abstract
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.
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Keywords: Bernoulli trial; embedding in Poisson process; random permutation; records; runs of successes; sums of indicators
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1261670698
Digital Object Identifier: doi:10.1239/jap/1261670698
Zentralblatt MATH identifier: 05665465
Mathematical Reviews number (MathSciNet): MR2582715
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Journal of Applied Probability
