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Published by Cambridge University Press, Cambridge, 2020
ISBN 10: 1107074681 ISBN 13: 9781107074682
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Hardcover. Condition: new. Hardcover. 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. This is a complete and systematic modern treatise on large deviation theory for random walks with light-tailed jump distributions, presented by one of its key creators. Such distributions have numerous applications in statistics, ruin theory, and queuing theory. This is a companion to the author's earlier monograph on heavy-tailed distributions. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
Published by Cambridge University Press, 2008
ISBN 10: 052188117X ISBN 13: 9780521881173
Language: English
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Add to basketHardcover. Condition: new. Hardcover. 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. This is a complete and systematic modern treatise on large deviation theory for random walks with light-tailed jump distributions, presented by one of its key creators. Such distributions have numerous applications in statistics, ruin theory, and queuing theory. This is a companion to the author's earlier monograph on heavy-tailed distributions. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.
Published by Cambridge University Press, 2008
ISBN 10: 052188117X ISBN 13: 9780521881173
Language: English
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Add to basketCondition: New. This is a complete and systematic modern treatise on large deviation theory for random walks with light-tailed jump distributions, presented by one of its key creators. Such distributions have numerous applications in statistics, ruin theory, and queuing th.
Published by Cambridge University Press, Cambridge, 2008
ISBN 10: 052188117X ISBN 13: 9780521881173
Language: English
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Hardcover. Condition: new. Hardcover. This book focuses on the asymptotic behavior 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. 'Heavy-tailed' distributions describe claim sizes in insurance, losses in finance, and more. In many applications, critically important events can be represented as 'large deviations' of random walks - computing probabilities of such events is essential. This monograph presents a unified systematic exposition of the large deviations theory for heavy-tailed random walks. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
Published by Cambridge University Press, 2008
ISBN 10: 052188117X ISBN 13: 9780521881173
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Add to basketHardcover. Condition: new. Hardcover. This book focuses on the asymptotic behavior 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. 'Heavy-tailed' distributions describe claim sizes in insurance, losses in finance, and more. In many applications, critically important events can be represented as 'large deviations' of random walks - computing probabilities of such events is essential. This monograph presents a unified systematic exposition of the large deviations theory for heavy-tailed random walks. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.
Published by Cambridge University Press Okt 2020, 2020
ISBN 10: 1107074681 ISBN 13: 9781107074682
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Published by Cambridge University Press, Cambridge, 2008
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Add to basketHardcover. Condition: new. Hardcover. This book focuses on the asymptotic behavior 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. 'Heavy-tailed' distributions describe claim sizes in insurance, losses in finance, and more. In many applications, critically important events can be represented as 'large deviations' of random walks - computing probabilities of such events is essential. This monograph presents a unified systematic exposition of the large deviations theory for heavy-tailed random walks. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.
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Add to basketHardcover. Condition: Brand New. 625 pages. 9.50x6.50x1.75 inches. In Stock.
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Add to basketBuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.
Published by Cambridge University Press, 2020
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Add to basketHardback. Condition: New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days 840.
Published by Cambridge University Press, 2020
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Published by Cambridge University Press, 2015
ISBN 10: 052188117X ISBN 13: 9780521881173
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Add to basketCondition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Heavy-tailed distributions describe claim sizes in insurance, losses in finance, and more. In many applications, critically important events can be represented as large deviations of random walks - computing probabilities of such events is essential. Th.