Holst, Lars A note on embedding certain Bernoulli sequences in marked Poisson processes. (English) Zbl 1154.60009 J. Appl. Probab. 45, No. 4, 1181-1185 (2008). Summary: A sequence of independent Bernoulli random variables with success probabilities \(a / (a + b + k - 1), k = 1, 2, 3, \dots \), is embedded in a marked Poisson process with intensity 1. Using this, conditional Poisson limits follow for counts of failure strings. Cited in 7 Documents MSC: 60C05 Combinatorial probability 60K99 Special processes Keywords:Bernoulli trial; conditional limit theorem; Poisson limit; random permutation; record; sums of indicators PDF BibTeX XML Cite \textit{L. Holst}, J. Appl. Probab. 45, No. 4, 1181--1185 (2008; Zbl 1154.60009) Full Text: DOI OpenURL References: [1] Arratia, R., Barbour, A. D. and Tavaré, S. (2003). Logarithmic Combinatorial Structures: A Probabilistic Approach. European Mathematical Society, Zürich. · Zbl 1040.60001 [2] Holst, L. (2007). Counts of failure strings in certain Bernoulli sequences. J. Appl. Prob. 44 , 824–830. · Zbl 1132.60011 [3] Holst, L. (2008). The number of two consecutive successes in a Hoppe–Pólya urn. J. Appl. Prob. 45 , 901–906. · Zbl 1151.60002 [4] 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. · Zbl 1165.60305 [5] Kingman, J. F. C (1993). Poisson Processes (Oxford Studies Prob. 3 ). Oxford University Press. · Zbl 0771.60001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.