A note on embedding certain Bernoulli sequences in marked Poisson processes. (English) Zbl 1154.60009

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.


60C05 Combinatorial probability
60K99 Special processes
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