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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


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 $\{Y_t, t \in T\}$ 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.


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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.


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

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

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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