## The Annals of Applied Probability

### Random USC Functions, Max-Stable Processes and Continuous Choice

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

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

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005937

Digital Object Identifier
doi:10.1214/aoap/1177005937

Mathematical Reviews number (MathSciNet)
MR1102320

Zentralblatt MATH identifier
0731.60079

JSTOR