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On infinite perfect graphs and randomized stopping points on the plane
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  • Published: July 1988

On infinite perfect graphs and randomized stopping points on the plane

  • Robert C. Dalang1 nAff2 

Probability Theory and Related Fields volume 78, pages 357–378 (1988)Cite this article

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  • 8 Citations

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Abstract

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.

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Author information

Author notes
  1. Robert C. Dalang

    Present address: Department of Statistics, University of California, 94720, Berkeley, CA, USA

Authors and Affiliations

  1. Département de Mathématiques, Ecole Polytechnique Fédérale, CH-1015, Lausanne, Switzerland

    Robert C. Dalang

Authors
  1. Robert C. Dalang
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Additional information

This research was accomplished while the author was visiting the School of Operations Research and Industrial Engineering at Cornell University and was supported by a grant from the “Fonds National Suisse pour la Recherche Scientifique”

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Cite this article

Dalang, R.C. On infinite perfect graphs and randomized stopping points on the plane. Probab. Th. Rel. Fields 78, 357–378 (1988). https://doi.org/10.1007/BF00334200

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  • Received: 05 June 1986

  • Revised: 27 January 1988

  • Issue Date: July 1988

  • DOI: https://doi.org/10.1007/BF00334200

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Keywords

  • Filtration
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Random Measure
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