Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice

Preface. Acknowledgments. INTRODUCTION. Random Vectors. Linear Operators. Infinitely Divisible Distributions and Triangular Arrays. MULTIVARIATE REGULAR VARIATION. Regular Variations for Linear Operators. Regular Variation for Real-Valued Functions. Regular Variation for Borel Measures. MULTIVARIATE LIMIT THEOREMS. The Limit Distributions. Central Limit Theorems. Related Limit Theorems. APPLICATIONS. Applications to Statistics. Self-Similar Stochastic Processes. References. Index.