Open Access
August, 1994 Superextremal Processes, Max-Stability and Dynamic Continuous Choice
Sidney I. Resnick, Rishin Roy
Ann. Appl. Probab. 4(3): 791-811 (August, 1994). DOI: 10.1214/aoap/1177004972

Abstract

A general framework in an ordinal utility setting for the analysis of dynamic choice from a continuum of alternatives E is proposed. The model is based on the theory of random utility maximization in continuous time. We work with superextremal processes Y={Yt,t(0,)}, where Yt={Yt(τ),τE} is a random element of the space of upper semicontinuous functions on a compact metric space E. Here Yt(τ) represents the utility at time t for alternative τE. The choice process M={Mt,t(0,)}, is studied, where Mt is the set of utility maximizing alternatives at time t, that is, Mt is the set of τE at which the sample paths of Yt on E achieve their maximum. Independence properties of Y and M are developed, and general conditions for M to have the Markov property are described. An example of such conditions is that Y have max-stable marginals.

Citation

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Sidney I. Resnick. Rishin Roy. "Superextremal Processes, Max-Stability and Dynamic Continuous Choice." Ann. Appl. Probab. 4 (3) 791 - 811, August, 1994. https://doi.org/10.1214/aoap/1177004972

Information

Published: August, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0809.60064
MathSciNet: MR1284986
Digital Object Identifier: 10.1214/aoap/1177004972

Subjects:
Primary: 60G70
Secondary: 60G55

Keywords: Choice theory , Extreme value theory , max-stability , Poisson process , superextremal processes

Rights: Copyright © 1994 Institute of Mathematical Statistics

Vol.4 • No. 3 • August, 1994
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