The Annals of Applied Probability

Random USC Functions, Max-Stable Processes and Continuous Choice

Sidney I. Resnick and Rishin Roy

Full-text: Open access


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.

Article information

Ann. Appl. Probab., Volume 1, Number 2 (1991), 267-292.

First available in Project Euclid: 19 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]

Choice theory extreme values extremal processes random closed sets random upper semicontinuous functions max-stable processes


Resnick, Sidney I.; Roy, Rishin. Random USC Functions, Max-Stable Processes and Continuous Choice. Ann. Appl. Probab. 1 (1991), no. 2, 267--292. doi:10.1214/aoap/1177005937.

Export citation