Excessive Measures:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
1990
|
| Series: | Probability and Its Applications
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The study of the cone of excessive measures associated with a Markov process goes back to Hunt's fundamental memoir [H57]. However until quite recently it received much less attention than the cone of excessive functions. The fact that an excessive function can be composed with the underlying Markov process to give a supermartingale, subject to secondary finiteness hypotheses, is crucial in the study of excessive functions. The lack of an analogous construct for excessive measures seemed to make them much less tractable to a probabilistic analysis. This point of view changed radically with the appearance of the pioneering paper by Fitzsimmons and Maisonneuve [FM86] who showed that a certain stationary process associated with an excessive measure could be used to study excessive measures probabilistically. These stationary processes or measures had been constructed by Kuznetsov [Ku74] extending earlier work of Dynkin. It is now common to call them Kuznetsov measures. Following the FitzsimmonsMaisonneuve paper there was renewed interest and remarkable progress in the study of excessive measures. The purpose of this monograph is to organize under one cover and prove under standard hypotheses many of these recent results in the theory of excessive measures. The two basic tools in this recent development are Kuznetsov measures mentioned above and the energy functional |
| Physical Description: | 1 Online-Ressource (X, 190 p) |
| ISBN: | 9781461234708 9781461280361 |
| DOI: | 10.1007/978-1-4612-3470-8 |
Staff View
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Record in the Search Index
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| author | Getoor, R. K. |
| author_facet | Getoor, R. K. |
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| author_sort | Getoor, R. K. |
| author_variant | r k g rk rkg |
| building | Verbundindex |
| bvnumber | BV042420133 |
| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)1184357258 (DE-599)BVBBV042420133 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-3470-8 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461234708 9781461280361 |
| language | English |
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| publishDate | 1990 |
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| spelling | Getoor, R. K. Verfasser aut Excessive Measures by R. K. Getoor Boston, MA Birkhäuser Boston 1990 1 Online-Ressource (X, 190 p) txt rdacontent c rdamedia cr rdacarrier Probability and Its Applications The study of the cone of excessive measures associated with a Markov process goes back to Hunt's fundamental memoir [H57]. However until quite recently it received much less attention than the cone of excessive functions. The fact that an excessive function can be composed with the underlying Markov process to give a supermartingale, subject to secondary finiteness hypotheses, is crucial in the study of excessive functions. The lack of an analogous construct for excessive measures seemed to make them much less tractable to a probabilistic analysis. This point of view changed radically with the appearance of the pioneering paper by Fitzsimmons and Maisonneuve [FM86] who showed that a certain stationary process associated with an excessive measure could be used to study excessive measures probabilistically. These stationary processes or measures had been constructed by Kuznetsov [Ku74] extending earlier work of Dynkin. It is now common to call them Kuznetsov measures. Following the FitzsimmonsMaisonneuve paper there was renewed interest and remarkable progress in the study of excessive measures. The purpose of this monograph is to organize under one cover and prove under standard hypotheses many of these recent results in the theory of excessive measures. The two basic tools in this recent development are Kuznetsov measures mentioned above and the energy functional Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Exzessives Maß (DE-588)4434832-0 gnd rswk-swf Exzessives Maß (DE-588)4434832-0 s 1\p DE-604 Markov-Prozess (DE-588)4134948-9 s 2\p DE-604 Maßtheorie (DE-588)4074626-4 s 3\p DE-604 https://doi.org/10.1007/978-1-4612-3470-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Getoor, R. K. Excessive Measures Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Markov-Prozess (DE-588)4134948-9 gnd Maßtheorie (DE-588)4074626-4 gnd Exzessives Maß (DE-588)4434832-0 gnd |
| subject_GND | (DE-588)4134948-9 (DE-588)4074626-4 (DE-588)4434832-0 |
| title | Excessive Measures |
| title_auth | Excessive Measures |
| title_exact_search | Excessive Measures |
| title_full | Excessive Measures by R. K. Getoor |
| title_fullStr | Excessive Measures by R. K. Getoor |
| title_full_unstemmed | Excessive Measures by R. K. Getoor |
| title_short | Excessive Measures |
| title_sort | excessive measures |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Markov-Prozess (DE-588)4134948-9 gnd Maßtheorie (DE-588)4074626-4 gnd Exzessives Maß (DE-588)4434832-0 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Markov-Prozess Maßtheorie Exzessives Maß |
| url | https://doi.org/10.1007/978-1-4612-3470-8 |
| work_keys_str_mv | AT getoorrk excessivemeasures |