Asymptotic analysis of random walks: light-tailed distributions
This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistic...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY
Cambridge University Press
2020
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| Schriftenreihe: | Encyclopedia of mathematics and its applications
176 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBA01 URL des Erstveröffentlichers |
| Zusammenfassung: | This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 29 Oct 2020) |
| Beschreibung: | 1 Online-Ressource (xvi, 419 Seiten) |
| ISBN: | 9781139871303 |
| DOI: | 10.1017/9781139871303 |
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| 245 | 1 | 0 | |a Asymptotic analysis of random walks |b light-tailed distributions |c A.A. Borovkov, Sobolev Institute of Mathematics, Novosibirsk ; translated by V.V. Ulyanov, Higher School of Economics, Mikhail Zhitlukhin, Steklov Institute of Mathematics, Moscow |
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| isbn | 9781139871303 |
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| spelling | Borovkov, A. A. 1931- Verfasser (DE-588)1089930224 aut Asymptotic analysis of random walks light-tailed distributions A.A. Borovkov, Sobolev Institute of Mathematics, Novosibirsk ; translated by V.V. Ulyanov, Higher School of Economics, Mikhail Zhitlukhin, Steklov Institute of Mathematics, Moscow Cambridge, United Kingdom ; New York, NY Cambridge University Press 2020 1 Online-Ressource (xvi, 419 Seiten) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications 176 Title from publisher's bibliographic system (viewed on 29 Oct 2020) This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Random walks (Mathematics) Asymptotic distribution (Probability theory) Asymptotic expansions Irrfahrtsproblem (DE-588)4162442-7 s Asymptotik (DE-588)4126634-1 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-107-07468-2 https://doi.org/10.1017/9781139871303 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Borovkov, A. A. 1931- Asymptotic analysis of random walks light-tailed distributions Irrfahrtsproblem (DE-588)4162442-7 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4162442-7 (DE-588)4126634-1 |
| title | Asymptotic analysis of random walks light-tailed distributions |
| title_auth | Asymptotic analysis of random walks light-tailed distributions |
| title_exact_search | Asymptotic analysis of random walks light-tailed distributions |
| title_exact_search_txtP | Asymptotic analysis of random walks light-tailed distributions |
| title_full | Asymptotic analysis of random walks light-tailed distributions A.A. Borovkov, Sobolev Institute of Mathematics, Novosibirsk ; translated by V.V. Ulyanov, Higher School of Economics, Mikhail Zhitlukhin, Steklov Institute of Mathematics, Moscow |
| title_fullStr | Asymptotic analysis of random walks light-tailed distributions A.A. Borovkov, Sobolev Institute of Mathematics, Novosibirsk ; translated by V.V. Ulyanov, Higher School of Economics, Mikhail Zhitlukhin, Steklov Institute of Mathematics, Moscow |
| title_full_unstemmed | Asymptotic analysis of random walks light-tailed distributions A.A. Borovkov, Sobolev Institute of Mathematics, Novosibirsk ; translated by V.V. Ulyanov, Higher School of Economics, Mikhail Zhitlukhin, Steklov Institute of Mathematics, Moscow |
| title_short | Asymptotic analysis of random walks |
| title_sort | asymptotic analysis of random walks light tailed distributions |
| title_sub | light-tailed distributions |
| topic | Irrfahrtsproblem (DE-588)4162442-7 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Irrfahrtsproblem Asymptotik |
| url | https://doi.org/10.1017/9781139871303 |
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