On sequential selection and a first passage problem for the Poisson process

2020/07/15 by Gnedin, Alexander
#60C05 #60J10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2007.07850

Abstract

This note is motivated by connections between the online and offline problems of selecting a possibly long subsequence from a Poisson-paced sequence of uniform marks under either a monotonicity or a sum constraint. The offline problem with the sum constraint amounts to counting the Poisson arrivals before their total exceeds a certain level. A precise asymptotics for the mean count is obtained by coupling with a nonlinear pure birth process.

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