Probabilities and potential C potential theory for discrete and continuous semigroups /
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 chapte...
| Main Author: | Dellacherie, Claude. |
|---|---|
| Other Authors: | Meyer, Paul André., ScienceDirect (Online service) |
| Format: | eBook |
| Language: | English French |
| Published: |
Amsterdam ; New York :
Elsevier,
1988.
|
| Physical Description: |
1 online resource (xiv, 416 pages) : illustrations. |
| Series: |
North-Holland mathematics studies ;
151. |
| Subjects: |
| 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 g̀̀ambling 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. |
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| Item Description: |
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 g̀̀ambling 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: Probabilités et potentiel C. Includes bibliographical references (pages 387-407) and indexes. Front Cover; Probabilities and Potential C; Copyright Page; Contents; CHAPTER IX. KERNELS AND EXCESSIVE FUNCTIONS; CHAPTER X. THEORY OF REDUCTIONS AND SWEEPING; CHAPTER XI. (APPENDIX TO CHAPTER X): NEW METHODS IN CAPACITY THEORY, APPLICATIONS TO GAMBLING HOUSES; CHAPTER XII. SEMIGROUPS AND RESOLVENTS; CHAPTER XIII. CONSTRUCTION OF RESOLVENTS AND SEMIGROUPS; COMMENTARIES AND HISTORICAL NOTES; BIBLIOGRAPHY; INDEX OF NOTATIONS; INDEX OF TERMINOLOGY; ADDITIONS AND CORRECTIONS TO THE PRECEDING VOLUMES. |
| Physical Description: |
1 online resource (xiv, 416 pages) : illustrations. |
| Bibliography: |
Includes bibliographical references (pages 387-407) and indexes. |
| ISBN: |
9780444703866 0444703861 9780080872629 008087262X |