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Monotone Case for an Extended Process

Part of: Stochastic processes

Published online by Cambridge University Press:  22 February 2016

Małgorzata Kuchta  and
Michał Morayne
Małgorzata Kuchta*
Affiliation:
Wrocław University of Technology
Michał Morayne*
Affiliation:
Wrocław University of Technology
*
∗ Postal address: Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
∗ Postal address: Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
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Abstract

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We consider a nonnegative discrete time and bounded horizon process X for which 0 is an absorbing state and extend it by a random variable that is independent of X. We find a sufficient condition for the resulting process to satisfy, after a canonical time rescaling, the hypothesis of the monotone case theorem. If X describes a secretary type search on a poset with one maximal element or if we consider X with no extension then this condition assumes an especially simple log-concavity type form.

Keywords

Monotone casesecretary problembest choiceoptimal stopping time

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 4 , December 2014 , pp. 1106 - 1125
Copyright
© Applied Probability Trust 

Footnotes

This research was partially supported by the MNiSW grant NN 206 36 9739.

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