Format:
Online-Ressource (XI, 157 p. 2 illus, digital)
Edition:
2nd ed. 2013
ISBN:
9781461471011
Series Statement:
Springer Series in Operations Research and Financial Engineering
Content:
Preface -- Introduction -- Heavy- and long-tailed distributions -- Subexponential distributions -- Densities and local probabilities -- Maximum of random walks -- References -- Index.
Content:
Heavy-tailed probability distributions are an important component in the modeling of many stochastic systems. They are frequently used to accurately model inputs and outputs of computer and data networks and service facilities such as call centers. They are an essential for describing risk processes in finance and also for insurance premia pricing, and such distributions occur naturally in models of epidemiological spread. The class includes distributions with power law tails such as the Pareto, as well as the lognormal and certain Weibull distributions. One of the highlights of this new edition is that it includes problems at the end of each chapter. Chapter 5 is also updated to include interesting applications to queueing theory, risk, and branching processes. New results are presented in a simple, coherent and systematic way. Graduate students as well as modelers in the fields of finance, insurance, network science and environmental studies will find this book to be an essential reference.
Note:
Description based upon print version of record
,
Preface to the First Edition; Preface; Contents; Notation and Conventions; Chapter 1 Introduction; Chapter 2 Heavy-Tailed and Long-Tailed Distributions; 2.1 Heavy-Tailed Distributions; 2.2 Characterisation of Heavy-Tailed Distributionsin Terms of Generalised Moments; 2.3 Lower Limit for Tails of Convolutions; 2.4 Long-Tailed Functions and Their Properties; 2.5 Long-Tailed Distributions; 2.6 Long-Tailed Distributions and Integrated Tails; 2.7 Convolutions of Long-Tailed Distributions; 2.8 h-Insensitive Distributions; 2.9 Comments; 2.10 Problems; Chapter 3 Subexponential Distributions
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3.1 Subexponential Distributions on the Positive Half-Line3.2 Subexponential Distributions on the Whole Real Line; 3.3 Subexponentiality and Weak Tail-Equivalence; 3.4 The Class S* of Strong Subexponential Distributions; 3.5 Sufficient Conditions for Subexponentiality; 3.6 Conditions for Subexponentiality in Termsof Truncated Exponential Moments; 3.7 S Is a Proper Subset of L; 3.8 Does FS Imply That FIS?; 3.9 Closure Properties of the Class of Subexponential Distributions; 3.10 Kesten's Bound; 3.11 Subexponentiality and Randomly Stopped Sums; 3.12 Comments; 3.13 Problems
,
Chapter 4 Densities and Local Probabilities4.1 Long Tailed Densities and Their Convolutions; 4.2 Subexponential Densities on the Positive Half-Line; 4.3 Subexponential Densities on the Real Line; 4.4 Sufficient Conditions for Subexponentiality of Densities; 4.5 bold0mu mumu dotted-Long-Tailed Distributions and Their Convolutions; 4.6 bold0mu mumu dotted-Subexponential Distributions; 4.7 bold0mu mumu dotted-Subexponential Distributions on the Real Line; 4.8 Sufficient Conditions for bold0mu mumu dotted-Subexponentiality; 4.9 Local Asymptotics for a Randomly Stopped Sum
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4.10 Local Subexponentiality of Integrated Tails4.11 Comments; 4.12 Problems; Chapter 5 Maximum of Random Walk; 5.1 Asymptotics for the Maximum of a Random Walkwith a Negative Drift; 5.2 Finite Time Horizon Asymptotics; 5.3 Ladder Structure of Maximum of Random Walk; 5.4 Taboo Renewal Measures; 5.5 Asymptotics for the First Ascending Ladder Height; 5.6 Tail of the Maximum Revisited; 5.7 Local Probabilities of the Maximum; 5.8 Density of the Maximum; 5.9 Explicitly Calculable Ascending Ladder Heights; 5.10 Single Server Queueing System; 5.11 Ruin Probabilities in Cramér-Lundberg Model
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5.12 Subcritical Branching Processes5.13 How Do Large Values of M Occur in Standard Cases?; 5.14 Comments; 5.15 Problems; Answers to Problems; References; Index
Additional Edition:
ISBN 9781461471004
Additional Edition:
Erscheint auch als Druck-Ausgabe Foss, Sergey An introduction to heavy-tailed and subexponential distributions New York : Springer, 2013 ISBN 9781461471004
Additional Edition:
ISBN 9781489988324
Language:
English
Subjects:
Mathematics
Keywords:
Subexponentielle Verteilung
;
Subexponentielle Verteilung
DOI:
10.1007/978-1-4614-7101-1
URL:
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