Excursions of Markov Processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1992
|
| Schriftenreihe: | Probability and Its Applications
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Let {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T < s < t. When one measures the time in t the zero set appropriately (in terms of the local time) the excursions acquire a measure theoretic structure practically identical to that of processes with stationary independent increments, except the values of the process are paths rather than real numbers. And there is a measure on path space that helps describe the measure theoretic properties of the excursions in the same way that the Levy measure describes the jumps of a process with independent increments. The entire circle of ideas is called excursion theory. There are many attractive things about the subject: it is an area where one can use to advantage general probabilistic potential theory to make quite specific calculations, it provides a natural setting for apply ing esoteric things like David Williams' path decomposition, it provides a method for constructing processes whose description in terms of an in finitesimal generator or some such analytic object would be complicated. And the ideas seem to be closely related to a good deal of current research in probability |
| Beschreibung: | 1 Online-Ressource (XII, 276 p) |
| ISBN: | 9781468494129 9781468494143 |
| DOI: | 10.1007/978-1-4684-9412-9 |
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| 100 | 1 | |a Blumenthal, Robert M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Excursions of Markov Processes |c by Robert M. Blumenthal |
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Datensatz im Suchindex
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| author | Blumenthal, Robert M. |
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| 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 | 10.1007/978-1-4684-9412-9 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468494129 9781468494143 |
| language | English |
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| spelling | Blumenthal, Robert M. Verfasser aut Excursions of Markov Processes by Robert M. Blumenthal Boston, MA Birkhäuser Boston 1992 1 Online-Ressource (XII, 276 p) txt rdacontent c rdamedia cr rdacarrier Probability and Its Applications Let {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T < s < t. When one measures the time in t the zero set appropriately (in terms of the local time) the excursions acquire a measure theoretic structure practically identical to that of processes with stationary independent increments, except the values of the process are paths rather than real numbers. And there is a measure on path space that helps describe the measure theoretic properties of the excursions in the same way that the Levy measure describes the jumps of a process with independent increments. The entire circle of ideas is called excursion theory. There are many attractive things about the subject: it is an area where one can use to advantage general probabilistic potential theory to make quite specific calculations, it provides a natural setting for apply ing esoteric things like David Williams' path decomposition, it provides a method for constructing processes whose description in terms of an in finitesimal generator or some such analytic object would be complicated. And the ideas seem to be closely related to a good deal of current research in probability Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s 1\p DE-604 https://doi.org/10.1007/978-1-4684-9412-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Blumenthal, Robert M. Excursions of Markov Processes Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4134948-9 |
| title | Excursions of Markov Processes |
| title_auth | Excursions of Markov Processes |
| title_exact_search | Excursions of Markov Processes |
| title_full | Excursions of Markov Processes by Robert M. Blumenthal |
| title_fullStr | Excursions of Markov Processes by Robert M. Blumenthal |
| title_full_unstemmed | Excursions of Markov Processes by Robert M. Blumenthal |
| title_short | Excursions of Markov Processes |
| title_sort | excursions of markov processes |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Markov-Prozess |
| url | https://doi.org/10.1007/978-1-4684-9412-9 |
| work_keys_str_mv | AT blumenthalrobertm excursionsofmarkovprocesses |