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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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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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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DOI: https://doi.org/10.1007/BF00334200
Keywords
- Filtration
- Stochastic Process
- Probability Theory
- Statistical Theory
- Random Measure