Regular, Sample Path and Strong Stochastic Convexity: A Review
Several notions of stochastic convexity and concavity and their properties are described in this survey. The notion of sample path stochastic convexity is a refinement of the well used notion of stochastic ordering, and it can be used to construct, on a common probability space, random variables whi...
| Veröffentlicht in: | Lecture Notes-Monograph Series. - Institute of Mathematical Statistics, 1982. - 19(1991) vom: Jan., Seite 320-333 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1991
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| Zugriff auf das übergeordnete Werk: | Lecture Notes-Monograph Series |
| Schlagworte: | Queueing theory Reliability theory Stochastic orderings Stochastic convexity Record values Branching processes Imperfect repair Mathematics Behavioral sciences Applied sciences |
| Zusammenfassung: | Several notions of stochastic convexity and concavity and their properties are described in this survey. The notion of sample path stochastic convexity is a refinement of the well used notion of stochastic ordering, and it can be used to construct, on a common probability space, random variables which have desirable convexity (or concavity) properties with probability one. Three open problems from the literature are described. These problems could not be resolved until the introduction of the stochastic convexity notions which are described in this survey. The solutions of these problems illustrate the strength and the usefulness of these notions. Each notion is accompanied by a description of some of its applications. References for more detailed study of these notions are given. Indications of further work in this area are included. |
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| ISSN: | 07492170 |