Probabilities and potential C [electronic resource] : potential theory for discrete and continuous semigroups / Claude Dellacherie and Paul-Andr�e Meyer ; translated and prepared by J. Norris.
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TextSeries: North-Holland mathematics studies ; 151.Publication details: Amsterdam ; New York : Elsevier, 1988. Description: 1 online resource (xiv, 416 p.) : illISBN: 9780444703866; 0444703861Subject(s): Probabilities | Potential theory (Mathematics) | Semigroups | Potential theory (Mathematics) | Probabilities | SemigroupsGenre/Form: Electronic books.Additional physical formats: Print version:: Probabilities and potential C.DDC classification: 519.2 LOC classification: QA273 | .D3713 1988ebOnline resources: ScienceDirect | Volltext Summary: This third volume of the monograph examines potential theory. The first chapter develops potential theory with respect to a single kernel (or discrete time semigroup). All the essential ideas of the theory are presented: excessive functions, reductions, sweeping, maximum principle. The second chapter begins with a study of the notion of reduction in the most general situation possible - the ``gambling house'' of Dubins and Savage. The beautiful results presented have never been made accessible to a wide public. These are then connected with the theory of sweeping with respect to a cone of continuous functions, and the integral representation in compact convex sets. The third chapter presents new or little-known results, with the aim of illustrating the effectiveness of capacitary methods in the most varied fields. The last two chapters are concerned with the theory of resolvents. The fourth and last part of the English edition will be devoted to the theory of Markov processes.
This third volume of the monograph examines potential theory. The first chapter develops potential theory with respect to a single kernel (or discrete time semigroup). All the essential ideas of the theory are presented: excessive functions, reductions, sweeping, maximum principle. The second chapter begins with a study of the notion of reduction in the most general situation possible - the ``gambling house'' of Dubins and Savage. The beautiful results presented have never been made accessible to a wide public. These are then connected with the theory of sweeping with respect to a cone of continuous functions, and the integral representation in compact convex sets. The third chapter presents new or little-known results, with the aim of illustrating the effectiveness of capacitary methods in the most varied fields. The last two chapters are concerned with the theory of resolvents. The fourth and last part of the English edition will be devoted to the theory of Markov processes.
Translation of: Probabilit�es et potentiel C.
Includes bibliographical references (p. 387-407) and indexes.
Description based on print version record.
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