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2021 On sequential selection and a first passage problem for the Poisson process
Alexander Gnedin
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Electron. Commun. Probab. 26: 1-13 (2021). DOI: 10.1214/21-ECP377

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.

Acknowledgments

The author is grateful Alex Marynych for a number of illuminating discussions. Thanks go to an anonymous referee for a pointer to the literature and contructive comments that lead to improvement of the presentattion.

Citation

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Alexander Gnedin. "On sequential selection and a first passage problem for the Poisson process." Electron. Commun. Probab. 26 1 - 13, 2021. https://doi.org/10.1214/21-ECP377

Information

Received: 21 July 2020; Accepted: 27 January 2021; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1214/21-ECP377

Subjects:
Primary: 60C05, 60G55, 60G80

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