On infinite perfect graphs and randomized stopping points on the plane
type: Item
instance of: scholarly article
title: On infinite perfect graphs and randomized stopping points on the plane
zbMATH Open document ID: 0628.60061
DOI: 10.1007/BF00334200
author: Robert C. Dalang
publication date: 1988-01-01T00:00:00Z
review text: We show that perfection of polytopes defined by infinite zero-one matrices can be characterized as in the finite case through an appropriate definition of infinite perfect graphs. We examine the relationship between certain such polytopes and a convex set of random measures on the discrete plane, termed randomized stopping points, that appear in the context of the optimal stopping problem for two-parameter processes. Using probabilistic techniques, we show that under a conditional qualitative independence hypothesis on the underlying filtration, which we express as a commutation property of a ``conditional supremum'' operator, the only extremal elements of this set of random measures are ordinary stopping points.
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 05C80
zbMATH DE Number: 4022291
zbMATH Keywords: infinite zero-one matrices
zbMATH Keywords: infinite perfect graphs
zbMATH Keywords: convex set of random measures
zbMATH Keywords: optimal stopping problems for two-parameter processes
zbMATH Keywords: extremal elements
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4022291