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

被引：1

作者：

Gnedin, Alexander ^{[1
]}

机构：

[1] Queen Mary Univ London, London, England

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2021年 / 26卷

关键词：

sequential selection; Poisson process; birth process; Borel distribution;

D O I：

10.1214/21-ECP377

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页数：13

共 50 条

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