An Introduction to Heavy-Tailed and Subexponential Distributions

This book provides a complete introduction to the theory of long tailed and subexponential distributions. This new edition includes problems at the end of each chapter.

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.

Provides a complete and comprehensive introduction to the theory of long tailed and subexponential distributions Expanded text features new exercises and numerous examples Includes preliminary mathematical material Includes supplementary material: sn.pub/extras

Autorentext

Sergey Foss is a professor at Heriot-Watt University, Edinburgh, UK. Dmitry Korshunov is a professor at the Sobolev Institute of Mathematics of the Russian Academy of Sciences, Novosibirsk, Russia. Stan Zachary is a professor at Heriot-Watt University, Edinburgh, UK.

Inhalt

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