This volume contains a unique collection of mathematical essays that resent 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 tailed modeling, running the gamut from insurance and finance, to telecommunications and the World Wide Web, and classical signal/noise detection problems. Preface ix(4) Contributors xiii I. Applications 3(130) Heavy-Tailed Probability Distributions in the World Wide Web 3(24) Mark E. Crovella Murad S. Taqqu Azer Bestavros Self-Similarity and Heavy Tails: Structural Modeling of Network Traffic 27(28) Walter Willinger Vern Paxson Murad S. Taqqu Heavy Tails in High-Frequency Financial Data 55(24) Ulrich A. Muller Michel M. Dacorogna Olivier V. Pictet Stable Paretian Modeling in Finance: Some Empirical and Theoretical Aspects 79(32) Stefan Mittnik Svetlozar T. Rachev Marc S. Paolella Risk Management and Quantile Estimation 111(22) Franco Bass Paul Embrechts Maria Kafetzaki II. Time Series 133 Analysing Stable Time Series 133(26) Robert J. Adler Raisa E. Feldman Colin Gallagher Inference for Linear Processes with Stable Noise 159(18) M. Calder R.A. Davis On Estimating the Intensity of Long-Range Dependence in Finite and Infinite Variance Time Series 177(42) Murad S. Taqqu Vadim Teverovsky Why Non-Linearities Can Ruin the Heavy-Tailed Modeler's Day 219 Sidney I. Resnick