Non-homogeneous random walks :: Lyapunov function methods for near-critical stochastic systems /
Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain cr...
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Hauptverfasser: | , , |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Cambridge :
Cambridge University Press,
2017.
|
Schriftenreihe: | Cambridge tracts in mathematics ;
209. |
Schlagworte: | |
Online-Zugang: | Volltext |
Zusammenfassung: | Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems. |
Beschreibung: | 1 online resource (xviii, 363 pages) : illustrations |
Bibliographie: | Includes bibliographical references and index. |
ISBN: | 9781316868980 1316868982 9781139208468 1139208462 |
Internformat
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245 | 1 | 0 | |a Non-homogeneous random walks : |b Lyapunov function methods for near-critical stochastic systems / |c Mikhail Menshikov, University of Durham ; Serguei Popov, Universidade Estadual de Campinas, Brazil ; Andrew Wade, University of Durham. |
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490 | 1 | |a Cambridge tracts in mathematics ; |v 209 | |
520 | |a Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems. | ||
504 | |a Includes bibliographical references and index. | ||
505 | 0 | |a Introduction -- Semimartingale approach and Markov chains -- Lamperti's problem -- Many-dimensional random walks -- Heavy tails -- Further applications -- Markov chains in continuous time. | |
588 | 0 | |a Print version record. | |
650 | 0 | |a Random walks (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85111357 | |
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650 | 7 | |a Procesos estocásticos |2 embne | |
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adam_text | |
any_adam_object | |
author | Menʹshikov, M. V. (Mikhail Vasilʹevich) Popov, Serguei, 1972- Wade, Andrew (Andrew R.), 1981- |
author_GND | http://id.loc.gov/authorities/names/n83221015 http://id.loc.gov/authorities/names/n2016044194 http://id.loc.gov/authorities/names/n2016044198 |
author_facet | Menʹshikov, M. V. (Mikhail Vasilʹevich) Popov, Serguei, 1972- Wade, Andrew (Andrew R.), 1981- |
author_role | aut aut aut |
author_sort | Menʹshikov, M. V. |
author_variant | m v m mv mvm s p sp a w aw |
building | Verbundindex |
bvnumber | localFWS |
callnumber-first | Q - Science |
callnumber-label | QA274 |
callnumber-raw | QA274.73 .M46 2017eb |
callnumber-search | QA274.73 .M46 2017eb |
callnumber-sort | QA 3274.73 M46 42017EB |
callnumber-subject | QA - Mathematics |
collection | ZDB-4-EBA |
contents | Introduction -- Semimartingale approach and Markov chains -- Lamperti's problem -- Many-dimensional random walks -- Heavy tails -- Further applications -- Markov chains in continuous time. |
ctrlnum | (OCoLC)968211509 |
dewey-full | 519.2/82 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.2/82 |
dewey-search | 519.2/82 |
dewey-sort | 3519.2 282 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Electronic eBook |
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id | ZDB-4-EBA-ocn968211509 |
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institution | BVB |
isbn | 9781316868980 1316868982 9781139208468 1139208462 |
language | English |
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series | Cambridge tracts in mathematics ; |
series2 | Cambridge tracts in mathematics ; |
spelling | Menʹshikov, M. V. (Mikhail Vasilʹevich), author. https://id.oclc.org/worldcat/entity/E39PBJktqgt7K6mQVkKJQ4X68C http://id.loc.gov/authorities/names/n83221015 Non-homogeneous random walks : Lyapunov function methods for near-critical stochastic systems / Mikhail Menshikov, University of Durham ; Serguei Popov, Universidade Estadual de Campinas, Brazil ; Andrew Wade, University of Durham. Cambridge : Cambridge University Press, 2017. ©2017 1 online resource (xviii, 363 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge tracts in mathematics ; 209 Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems. Includes bibliographical references and index. Introduction -- Semimartingale approach and Markov chains -- Lamperti's problem -- Many-dimensional random walks -- Heavy tails -- Further applications -- Markov chains in continuous time. Print version record. Random walks (Mathematics) http://id.loc.gov/authorities/subjects/sh85111357 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Marches aléatoires (Mathématiques) Processus stochastiques. MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Procesos estocásticos embne Random walks (Mathematics) fast Stochastic processes fast Electronic books. Popov, Serguei, 1972- author. https://id.oclc.org/worldcat/entity/E39PCjtKbWYckTMq8YWkt4HWfy http://id.loc.gov/authorities/names/n2016044194 Wade, Andrew (Andrew R.), 1981- author. https://id.oclc.org/worldcat/entity/E39PCjHG9jjbykkyCvytqDMK8d http://id.loc.gov/authorities/names/n2016044198 has work: Non-homogeneous random walks (Text) https://id.oclc.org/worldcat/entity/E39PCGp4Y9mcQT8XgKP3vvQBxC https://id.oclc.org/worldcat/ontology/hasWork Print version: Menʹshikov, M.V. (Mikhail Vasilʹevich). Non-homogeneous random walks. Cambridge, United Kingdom : Cambridge University Press, 2017 9781107026698 (DLC) 2016036262 (OCoLC)956946977 Cambridge tracts in mathematics ; 209. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1450860 Volltext |
spellingShingle | Menʹshikov, M. V. (Mikhail Vasilʹevich) Popov, Serguei, 1972- Wade, Andrew (Andrew R.), 1981- Non-homogeneous random walks : Lyapunov function methods for near-critical stochastic systems / Cambridge tracts in mathematics ; Introduction -- Semimartingale approach and Markov chains -- Lamperti's problem -- Many-dimensional random walks -- Heavy tails -- Further applications -- Markov chains in continuous time. Random walks (Mathematics) http://id.loc.gov/authorities/subjects/sh85111357 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Marches aléatoires (Mathématiques) Processus stochastiques. MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Procesos estocásticos embne Random walks (Mathematics) fast Stochastic processes fast |
subject_GND | http://id.loc.gov/authorities/subjects/sh85111357 http://id.loc.gov/authorities/subjects/sh85128181 |
title | Non-homogeneous random walks : Lyapunov function methods for near-critical stochastic systems / |
title_auth | Non-homogeneous random walks : Lyapunov function methods for near-critical stochastic systems / |
title_exact_search | Non-homogeneous random walks : Lyapunov function methods for near-critical stochastic systems / |
title_full | Non-homogeneous random walks : Lyapunov function methods for near-critical stochastic systems / Mikhail Menshikov, University of Durham ; Serguei Popov, Universidade Estadual de Campinas, Brazil ; Andrew Wade, University of Durham. |
title_fullStr | Non-homogeneous random walks : Lyapunov function methods for near-critical stochastic systems / Mikhail Menshikov, University of Durham ; Serguei Popov, Universidade Estadual de Campinas, Brazil ; Andrew Wade, University of Durham. |
title_full_unstemmed | Non-homogeneous random walks : Lyapunov function methods for near-critical stochastic systems / Mikhail Menshikov, University of Durham ; Serguei Popov, Universidade Estadual de Campinas, Brazil ; Andrew Wade, University of Durham. |
title_short | Non-homogeneous random walks : |
title_sort | non homogeneous random walks lyapunov function methods for near critical stochastic systems |
title_sub | Lyapunov function methods for near-critical stochastic systems / |
topic | Random walks (Mathematics) http://id.loc.gov/authorities/subjects/sh85111357 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Marches aléatoires (Mathématiques) Processus stochastiques. MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Procesos estocásticos embne Random walks (Mathematics) fast Stochastic processes fast |
topic_facet | Random walks (Mathematics) Stochastic processes. Marches aléatoires (Mathématiques) Processus stochastiques. MATHEMATICS Applied. MATHEMATICS Probability & Statistics General. Procesos estocásticos Stochastic processes Electronic books. |
url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1450860 |
work_keys_str_mv | AT menʹshikovmv nonhomogeneousrandomwalkslyapunovfunctionmethodsfornearcriticalstochasticsystems AT popovserguei nonhomogeneousrandomwalkslyapunovfunctionmethodsfornearcriticalstochasticsystems AT wadeandrew nonhomogeneousrandomwalkslyapunovfunctionmethodsfornearcriticalstochasticsystems |