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May, 1991 Random USC Functions, Max-Stable Processes and Continuous Choice
Sidney I. Resnick, Rishin Roy
Ann. Appl. Probab. 1(2): 267-292 (May, 1991). DOI: 10.1214/aoap/1177005937

Abstract

The theory of random utility maximization for a finite set of alternatives is generalized to alternatives which are elements of a compact metric space T. We model the random utility of these alternatives ranging over a continuum as a random process {Yt,tT} with upper semicontinuous (usc) sample paths. The alternatives which achieve the maximum utility levels constitute a random closed, compact set M. We specialize to a model where the random utility is a max-stable process with a.s. usc paths. Further path properties of these processes are derived and explicit formulas are calculated for the hitting and containment functionals of M. The hitting functional corresponds to the choice probabilities.

Citation

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Sidney I. Resnick. Rishin Roy. "Random USC Functions, Max-Stable Processes and Continuous Choice." Ann. Appl. Probab. 1 (2) 267 - 292, May, 1991. https://doi.org/10.1214/aoap/1177005937

Information

Published: May, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0731.60079
MathSciNet: MR1102320
Digital Object Identifier: 10.1214/aoap/1177005937

Subjects:
Primary: 60K10
Secondary: 60J20

Keywords: Choice theory , extremal processes , Extreme values , max-stable processes , random closed sets , random upper semicontinuous functions

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.1 • No. 2 • May, 1991
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