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August, 1977 The Infinite Secretary Problem as the Limit of the Finite Problem
Jacqueline Gianini
Ann. Probab. 5(4): 636-644 (August, 1977). DOI: 10.1214/aop/1176995775

Abstract

In a recent paper by J. Gianini and S. M. Samuels an "infinite secretary problem" was formulated: an infinite, countable sequence of rankable individuals (rank 1 = best) arrive at times which are independent and uniformly distributed on [0, 1]. As they arrive, only their relative ranks with respect to their predecessors can be observed. Given an increasing cost function $q(\bullet)$, let $\nu$ be the minimum, among all stopping rules, of the mean of the function $q$ of the actual rank of the individual chosen. Let $\nu(n)$ be the corresponding minimum for a finite secretary problem with $n$ individuals. Then $\lim \nu(n) = \nu$.

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Jacqueline Gianini. "The Infinite Secretary Problem as the Limit of the Finite Problem." Ann. Probab. 5 (4) 636 - 644, August, 1977. https://doi.org/10.1214/aop/1176995775

Information

Published: August, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0371.60054
MathSciNet: MR443072
Digital Object Identifier: 10.1214/aop/1176995775

Subjects:
Primary: 60G40

Keywords: convergence , Optimal stopping rules

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 4 • August, 1977
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