1652404805

An Introduction to Heavy-Tailed and Subexponential Distributions / by Sergey Foss, Dmitry Korshunov, Stan Zachary

Korshunov, Dmitry ; Zachary, Stan

2nd ed. 2013

Englisch

New York, NY : Springer New York, 2013

Online-Ressource (XI, 157 p. 2 illus, digital)

Description based upon print version of record

Druckausg.: An introduction to heavy-tailed and subexponential distributions. - New York : Springer, 2013. - XI, 157 S.

978-1-4614-7101-1

Weitere Ausgaben: 978-1-4614-7100-4 (Druckausgabe)

DOI: 10.1007/978-1-4614-7101-1

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

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

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

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

*Subexponentielle Verteilung

*Subexponentielle Verteilung

*Distribution (Probability theory) ; Economics -- Statistics ; Mathematics ; Probabilities. ; Statistics . ; Statistical physics. ; Dynamical systems. ; Mathematics ; Distribution (Probability theory) ; Economics -- Statistics

Klassifikation der Library of Congress: QA273.A1-274.9 ; QA274-274.9 ; QA273.A1-274.9 ; QA274-274.9

Dewey Dezimal-Klassifikation: 519.2; ; 519.24;

Dewey Dezimal-Klassifikation: 519.2

Regensburger Verbund-Klassifikation: SK 835: SA-SP Mathematik / SK Monografien / SK 800 Wahrscheinlichkeitstheorie / Wahrscheinlichkeitsverteilung

Book Industry Communication: PBWL

Book Industry Communication: PBT

bisacsh: MAT029000

Mathematics Subject Classification: *62-01

Mathematics Subject Classification: 62G32

Mathematics Subject Classification: 62E10

Mathematics Subject Classification: 62Pxx

Preface -- Introduction -- Heavy- and long-tailed distributions -- Subexponential distributions -- Densities and local probabilities -- Maximum of random walks -- References -- Index.

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.

https://zbmath.org/?q=an:1274.62005 [Zentralblatt MATH]

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https://doi.org/10.1007/978-1-4614-7101-1 [E-books (Springer)]