Markov Processes: Volume 1
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1965
|
| Schriftenreihe: | Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete
121/122 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The modem theory of Markov processes has its origins in the studies of A. A. MARKOV (1906-1907) on sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian motion (L. BACHELlER 1900, A. EIN STEIN 1905). The first correct mathematical construction of a Markov process with continuous trajectories was given by N. WIENER in 1923. (This process is often called the Wiener process.) The general theory of Markov processes was developed in the 1930's and 1940's by A. N. KOL MOGOROV, W. FELLER, W. DOEBLlN, P. LEVY, J. L. DOOB, and others. During the past ten years the theory of Markov processes has entered a new period of intensive development. The methods of the theory of semigroups of linear operators made possible further progress in the classification of Markov processes by their infinitesimal characteristics. The broad classes of Markov processes with continuous trajectories be came the main object of study. The connections between Markov pro cesses and classical analysis were further developed. It has become possible not only to apply the results and methods of analysis to the problems of probability theory, but also to investigate analytic problems using probabilistic methods. Remarkable new connections between Markov processes and potential theory were revealed. The foundations of the theory were reviewed critically: the new concept of strong Markov process acquired for the whole theory of Markov processes great importance |
| Beschreibung: | 1 Online-Ressource (XII, 366 p.) 1 illus |
| ISBN: | 9783662000311 9783662000335 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-00031-1 |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-00031-1 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783662000311 9783662000335 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858589 |
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| physical | 1 Online-Ressource (XII, 366 p.) 1 illus |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1965 |
| publishDateSearch | 1965 |
| publishDateSort | 1965 |
| publisher | Springer Berlin Heidelberg |
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| series2 | Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Dynkin, E. B. Verfasser aut Markov Processes Volume 1 by E. B. Dynkin Berlin, Heidelberg Springer Berlin Heidelberg 1965 1 Online-Ressource (XII, 366 p.) 1 illus txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete 121/122 0072-7830 The modem theory of Markov processes has its origins in the studies of A. A. MARKOV (1906-1907) on sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian motion (L. BACHELlER 1900, A. EIN STEIN 1905). The first correct mathematical construction of a Markov process with continuous trajectories was given by N. WIENER in 1923. (This process is often called the Wiener process.) The general theory of Markov processes was developed in the 1930's and 1940's by A. N. KOL MOGOROV, W. FELLER, W. DOEBLlN, P. LEVY, J. L. DOOB, and others. During the past ten years the theory of Markov processes has entered a new period of intensive development. The methods of the theory of semigroups of linear operators made possible further progress in the classification of Markov processes by their infinitesimal characteristics. The broad classes of Markov processes with continuous trajectories be came the main object of study. The connections between Markov pro cesses and classical analysis were further developed. It has become possible not only to apply the results and methods of analysis to the problems of probability theory, but also to investigate analytic problems using probabilistic methods. Remarkable new connections between Markov processes and potential theory were revealed. The foundations of the theory were reviewed critically: the new concept of strong Markov process acquired for the whole theory of Markov processes great importance Mathematics Mathematics, general Mathematik https://doi.org/10.1007/978-3-662-00031-1 Verlag Volltext |
| spellingShingle | Dynkin, E. B. Markov Processes Volume 1 Mathematics Mathematics, general Mathematik |
| title | Markov Processes Volume 1 |
| title_auth | Markov Processes Volume 1 |
| title_exact_search | Markov Processes Volume 1 |
| title_full | Markov Processes Volume 1 by E. B. Dynkin |
| title_fullStr | Markov Processes Volume 1 by E. B. Dynkin |
| title_full_unstemmed | Markov Processes Volume 1 by E. B. Dynkin |
| title_short | Markov Processes |
| title_sort | markov processes volume 1 |
| title_sub | Volume 1 |
| topic | Mathematics Mathematics, general Mathematik |
| topic_facet | Mathematics Mathematics, general Mathematik |
| url | https://doi.org/10.1007/978-3-662-00031-1 |
| work_keys_str_mv | AT dynkineb markovprocessesvolume1 |