This volume contains a unique collection of mathematical essays which present a battery of techniques and approaches for the statistical analysis of heavy tailed distributions and processes. The articles cover a number of applications of heavy tailedmodeling, running the gamut from insurance and finance, to telecommunications and the World Wide Web, and classical signal/noise detection problems. Along with the specific applications are several articles covering such areas as time series analysis in the heavy tailed setting, regression, and the general structure of stable processes as viewed from a modeling standpoint. Considerable emphasis is placed on recent developments in handling the numerical problems associated with stable distributions, which have been, until recently, one of the main technical difficulties in working in the heavy tailed setting. The papers are intended to be accessible to the widest possible audience, with an emphasis on applicability rather than...

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