Monotone Case for an Extended Process

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 c...

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Bibliographic Details
Published in:	Advances in applied probability Vol. 46; no. 4; pp. 1106 - 1125
Main Authors:	Kuchta, Małgorzata, Morayne, Michał
Format:	Journal Article
Language:	English
Published:	Cambridge, UK Cambridge University Press 01-12-2014 Applied Probability Trust
Subjects:	60G40 A priori knowledge best choice Discrete mathematics Expected values General Applied Probability Hasse diagrams Mathematical moments Mathematical theorems Monotone case optimal stopping time Partially ordered sets Probability Random variables secretary problem Stochastic processes Stopping distances Studies Theorems Monotone case optimal stopping time best choice 60G40 secretary problem
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Summary:	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.
ISSN:	0001-8678 1475-6064
DOI:	10.1239/aap/1418396245