Asymptotic analysis of random walks :: heavy-tailed distributions /
This monograph is devoted to studying 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. It presents a unified and systematic exposition.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English Russian |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2008.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
no. 118. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This monograph is devoted to studying 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. It presents a unified and systematic exposition. |
| Beschreibung: | 1 online resource (xxix, 625 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781461941576 1461941571 9780511826276 0511826273 9780511721397 0511721390 9781107390522 1107390524 1139883453 9781139883450 1107384095 9781107384095 1107387604 9781107387607 1107398932 9781107398931 1107395321 9781107395329 |
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| 245 | 1 | 0 | |a Asymptotic analysis of random walks : |b heavy-tailed distributions / |c A.A. Borovkov, K.A. Borovkov ; translated by O.B. Borovkova. |
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v number 118 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |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 | 8 | |a This monograph is devoted to studying 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. It presents a unified and systematic exposition. | |
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 650 | 0 | |a Random walks (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85111357 | |
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Datensatz im Suchindex
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| adam_text | |
| any_adam_object | |
| author | Borovkov, A. A. (Aleksandr Alekseevich), 1931- |
| author2 | Borovkov, K. A. (Konstantin Aleksandrovich) |
| author2_role | |
| author2_variant | k a b ka kab |
| author_GND | http://id.loc.gov/authorities/names/n80116978 http://id.loc.gov/authorities/names/n93117276 |
| author_facet | Borovkov, A. A. (Aleksandr Alekseevich), 1931- Borovkov, K. A. (Konstantin Aleksandrovich) |
| author_role | |
| author_sort | Borovkov, A. A. 1931- |
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| collection | ZDB-4-EBA |
| 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 | (OCoLC)857769752 |
| 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 |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn857769752 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:31Z |
| institution | BVB |
| isbn | 9781461941576 1461941571 9780511826276 0511826273 9780511721397 0511721390 9781107390522 1107390524 1139883453 9781139883450 1107384095 9781107384095 1107387604 9781107387607 1107398932 9781107398931 1107395321 9781107395329 |
| language | English Russian |
| oclc_num | 857769752 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxix, 625 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Borovkov, A. A. (Aleksandr Alekseevich), 1931- https://id.oclc.org/worldcat/entity/E39PBJhdcvmpbJ4Hq8GjKtQpfq http://id.loc.gov/authorities/names/n80116978 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) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; number 118 Includes bibliographical references and index. 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 monograph is devoted to studying 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. It presents a unified and systematic exposition. Print version record. English. Random walks (Mathematics) http://id.loc.gov/authorities/subjects/sh85111357 Asymptotic expansions. http://id.loc.gov/authorities/subjects/sh85009056 Marches aléatoires (Mathématiques) Développements asymptotiques. MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Asymptotic expansions fast Random walks (Mathematics) fast Asymptotik gnd http://d-nb.info/gnd/4126634-1 Irrfahrtsproblem gnd http://d-nb.info/gnd/4162442-7 Borovkov, K. A. (Konstantin Aleksandrovich) https://id.oclc.org/worldcat/entity/E39PCjGkBQtWxCjqYdXfwBPc8y http://id.loc.gov/authorities/names/n93117276 Print version: Borovkov, A.A. (Aleksandr Alekseevich), 1931- Asymptotic analysis of random walks 9780521881173 (DLC) 2008298018 (OCoLC)174130608 Encyclopedia of mathematics and its applications ; no. 118. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=616976 Volltext |
| spellingShingle | Borovkov, A. A. (Aleksandr Alekseevich), 1931- Asymptotic analysis of random walks : heavy-tailed distributions / Encyclopedia of mathematics and its applications ; 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) http://id.loc.gov/authorities/subjects/sh85111357 Asymptotic expansions. http://id.loc.gov/authorities/subjects/sh85009056 Marches aléatoires (Mathématiques) Développements asymptotiques. MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Asymptotic expansions fast Random walks (Mathematics) fast Asymptotik gnd http://d-nb.info/gnd/4126634-1 Irrfahrtsproblem gnd http://d-nb.info/gnd/4162442-7 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85111357 http://id.loc.gov/authorities/subjects/sh85009056 http://d-nb.info/gnd/4126634-1 http://d-nb.info/gnd/4162442-7 |
| 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) http://id.loc.gov/authorities/subjects/sh85111357 Asymptotic expansions. http://id.loc.gov/authorities/subjects/sh85009056 Marches aléatoires (Mathématiques) Développements asymptotiques. MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Asymptotic expansions fast Random walks (Mathematics) fast Asymptotik gnd http://d-nb.info/gnd/4126634-1 Irrfahrtsproblem gnd http://d-nb.info/gnd/4162442-7 |
| topic_facet | Random walks (Mathematics) Asymptotic expansions. Marches aléatoires (Mathématiques) Développements asymptotiques. MATHEMATICS Applied. MATHEMATICS Probability & Statistics General. Asymptotic expansions Asymptotik Irrfahrtsproblem |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=616976 |
| work_keys_str_mv | AT borovkovaa asymptoticanalysisofrandomwalksheavytaileddistributions AT borovkovka asymptoticanalysisofrandomwalksheavytaileddistributions |