Sistema Bibliotecario de la Universidad de Quintana Roo

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 modelingof 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 describingrisk 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 asthe Pareto, as well as the lognormal and certain Weibull distributions. This monograph defines the classes oflong-tailed and subexponential distributions in one dimension and provides a complete and comprehensive description of their properties. New results are presented in a simple, coherent and systematic way. This leads to a comprehensive exposition of tail properties of sums of independent random variables whose distributions belong to the long-tailed and subexponential class. The book includes adiscussion of and references to contemporary areas of applications and also contains preliminary mathematicalmaterialwhich makes the book self contained. Modelers in the fields of finance, insurance, network science and environmental studies will find this book to be an essential reference.

ZDB-2-SMA