Asymptotic analysis of random walks: heavy-tailed distributions
This book focuses on the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous ap...
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| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
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Cambridge
Cambridge University Press
2008
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| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 118 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This book focuses on the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous applied areas, typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer-overflow probabilities in queueing theory. The classical large deviation theory, developed for distributions decaying exponentially fast (or even faster) at infinity, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then direct probabilistic methods usually prove to be efficient. This monograph presents a unified and systematic exposition of the large deviation theory for heavy-tailed random walks. Most of the results presented in the book are appearing in a monograph for the first time. Many of them were obtained by the authors |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xxix, 625 pages) |
| ISBN: | 9780511721397 |
| DOI: | 10.1017/CBO9780511721397 |
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| 505 | 8 | |a Preliminaries -- Random walks with jumps having no finite first moment -- Random walks with jumps having finite mean and infinite variance -- Random walks with jumps having finite variance -- Random walks with semiexponential jump distributions -- Large deviations on the boundary of and outside the Cramer zone for random walks with jump distributions decaying exponentially fast -- Asymptotic properties of functions of regularly varying and semiexponential distributions. Asymptotics of the distributions of stopped sums and their maxima. An alternative approach to studying the asymptotics of P(S[subscript n] [is equal to or greater than] x) -- On the asymptotics of the first hitting times -- Integro-local and integral large deviation theorems for sums of random vectors -- Large deviations in trajectory space -- Large deviations of sums of random variables of two types -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of infinite second moment. Transient phenomena -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of finite variances -- Random walks with dependent jumps -- Extension of the results of Chapters 2-5 to continuous-time random processes with independent increments -- Extension of the results of Chapters 3 and 4 to generalized renewal processes | |
| 520 | |a This book focuses on the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous applied areas, typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer-overflow probabilities in queueing theory. The classical large deviation theory, developed for distributions decaying exponentially fast (or even faster) at infinity, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then direct probabilistic methods usually prove to be efficient. This monograph presents a unified and systematic exposition of the large deviation theory for heavy-tailed random walks. Most of the results presented in the book are appearing in a monograph for the first time. Many of them were obtained by the authors | ||
| 650 | 4 | |a Random walks (Mathematics) | |
| 650 | 4 | |a Asymptotic expansions | |
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Datensatz im Suchindex
| _version_ | 1804176883531644928 |
|---|---|
| any_adam_object | |
| author | Borovkov, A. A. 1931- |
| author2 | Borovkov, Konstantin A. Borovkova, O. B. |
| author2_role | edt trl |
| author2_variant | k a b ka kab o b b ob obb |
| author_GND | (DE-588)1089930224 (DE-588)1055786600 (DE-588)1292531061 |
| author_facet | Borovkov, A. A. 1931- Borovkov, Konstantin A. Borovkova, O. B. |
| author_role | aut |
| author_sort | Borovkov, A. A. 1931- |
| author_variant | a a b aa aab |
| building | Verbundindex |
| bvnumber | BV043941582 |
| classification_rvk | SK 820 |
| collection | ZDB-20-CBO |
| contents | Preliminaries -- Random walks with jumps having no finite first moment -- Random walks with jumps having finite mean and infinite variance -- Random walks with jumps having finite variance -- Random walks with semiexponential jump distributions -- Large deviations on the boundary of and outside the Cramer zone for random walks with jump distributions decaying exponentially fast -- Asymptotic properties of functions of regularly varying and semiexponential distributions. Asymptotics of the distributions of stopped sums and their maxima. An alternative approach to studying the asymptotics of P(S[subscript n] [is equal to or greater than] x) -- On the asymptotics of the first hitting times -- Integro-local and integral large deviation theorems for sums of random vectors -- Large deviations in trajectory space -- Large deviations of sums of random variables of two types -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of infinite second moment. Transient phenomena -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of finite variances -- Random walks with dependent jumps -- Extension of the results of Chapters 2-5 to continuous-time random processes with independent increments -- Extension of the results of Chapters 3 and 4 to generalized renewal processes |
| ctrlnum | (ZDB-20-CBO)CR9780511721397 (OCoLC)851089431 (DE-599)BVBBV043941582 |
| dewey-full | 519.282 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.282 |
| dewey-search | 519.282 |
| dewey-sort | 3519.282 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511721397 |
| format | Electronic eBook |
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| id | DE-604.BV043941582 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511721397 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350552 |
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| spelling | Borovkov, A. A. 1931- (DE-588)1089930224 aut Asymptotic analysis of random walks heavy-tailed distributions A.A. Borovkov, K.A. Borovkov ; translated by O.B. Borovkova Cambridge Cambridge University Press 2008 1 online resource (xxix, 625 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 118 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Preliminaries -- Random walks with jumps having no finite first moment -- Random walks with jumps having finite mean and infinite variance -- Random walks with jumps having finite variance -- Random walks with semiexponential jump distributions -- Large deviations on the boundary of and outside the Cramer zone for random walks with jump distributions decaying exponentially fast -- Asymptotic properties of functions of regularly varying and semiexponential distributions. Asymptotics of the distributions of stopped sums and their maxima. An alternative approach to studying the asymptotics of P(S[subscript n] [is equal to or greater than] x) -- On the asymptotics of the first hitting times -- Integro-local and integral large deviation theorems for sums of random vectors -- Large deviations in trajectory space -- Large deviations of sums of random variables of two types -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of infinite second moment. Transient phenomena -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of finite variances -- Random walks with dependent jumps -- Extension of the results of Chapters 2-5 to continuous-time random processes with independent increments -- Extension of the results of Chapters 3 and 4 to generalized renewal processes This book focuses on the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous applied areas, typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer-overflow probabilities in queueing theory. The classical large deviation theory, developed for distributions decaying exponentially fast (or even faster) at infinity, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then direct probabilistic methods usually prove to be efficient. This monograph presents a unified and systematic exposition of the large deviation theory for heavy-tailed random walks. Most of the results presented in the book are appearing in a monograph for the first time. Many of them were obtained by the authors Random walks (Mathematics) Asymptotic expansions Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Irrfahrtsproblem (DE-588)4162442-7 s Asymptotik (DE-588)4126634-1 s 1\p DE-604 Borovkov, Konstantin A. (DE-588)1055786600 edt Borovkova, O. B. (DE-588)1292531061 trl Erscheint auch als Druck-Ausgabe 978-0-521-88117-3 https://doi.org/10.1017/CBO9780511721397 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Borovkov, A. A. 1931- Asymptotic analysis of random walks heavy-tailed distributions Preliminaries -- Random walks with jumps having no finite first moment -- Random walks with jumps having finite mean and infinite variance -- Random walks with jumps having finite variance -- Random walks with semiexponential jump distributions -- Large deviations on the boundary of and outside the Cramer zone for random walks with jump distributions decaying exponentially fast -- Asymptotic properties of functions of regularly varying and semiexponential distributions. Asymptotics of the distributions of stopped sums and their maxima. An alternative approach to studying the asymptotics of P(S[subscript n] [is equal to or greater than] x) -- On the asymptotics of the first hitting times -- Integro-local and integral large deviation theorems for sums of random vectors -- Large deviations in trajectory space -- Large deviations of sums of random variables of two types -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of infinite second moment. Transient phenomena -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of finite variances -- Random walks with dependent jumps -- Extension of the results of Chapters 2-5 to continuous-time random processes with independent increments -- Extension of the results of Chapters 3 and 4 to generalized renewal processes Random walks (Mathematics) Asymptotic expansions 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 heavy-tailed distributions |
| title_auth | Asymptotic analysis of random walks heavy-tailed distributions |
| title_exact_search | Asymptotic analysis of random walks heavy-tailed distributions |
| title_full | Asymptotic analysis of random walks heavy-tailed distributions A.A. Borovkov, K.A. Borovkov ; translated by O.B. Borovkova |
| title_fullStr | Asymptotic analysis of random walks heavy-tailed distributions A.A. Borovkov, K.A. Borovkov ; translated by O.B. Borovkova |
| title_full_unstemmed | Asymptotic analysis of random walks heavy-tailed distributions A.A. Borovkov, K.A. Borovkov ; translated by O.B. Borovkova |
| title_short | Asymptotic analysis of random walks |
| title_sort | asymptotic analysis of random walks heavy tailed distributions |
| title_sub | heavy-tailed distributions |
| topic | Random walks (Mathematics) Asymptotic expansions Irrfahrtsproblem (DE-588)4162442-7 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Random walks (Mathematics) Asymptotic expansions Irrfahrtsproblem Asymptotik |
| url | https://doi.org/10.1017/CBO9780511721397 |
| work_keys_str_mv | AT borovkovaa asymptoticanalysisofrandomwalksheavytaileddistributions AT borovkovkonstantina asymptoticanalysisofrandomwalksheavytaileddistributions AT borovkovaob asymptoticanalysisofrandomwalksheavytaileddistributions |