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

ISBN-13: 9780471356295 / Angielski / Twarda / 2001 / 512 str.

Mark M. Meerschaert; Hans-Peter Scheffler; Hans-Peter Scheffler

Opis

A comprehensive introduction to the central limit theory-from foundations to current research
This volume provides an introduction to the central limit theory of random vectors, which lies at the heart of probability and statistics. The authors develop the central limit theory in detail, starting with the basic constructions of modern probability theory, then developing the fundamental tools of infinitely divisible distributions and regular variation. They provide a number of extensions and applications to probability and statistics, and take the reader through the fundamentals to the current level of research.
In synthesizing results from nearly 200 research papers and presenting them in a self-contained form, authors Meerschaert and Scheffler have produced an accessible reference that treats the central limit theory honestly and focuses on multivariate models. For researchers, it provides an efficient and logical path through a large collection of results with many possible applications to real-world phenomena. Limit Distributions for Sums of Independent Random Vectors includes a coherent introduction to limit distributions and these other features:
* A self-contained introduction to the multivariate problem
* Multivariate regular variation for linear operators, real-valued functions, and Borel Measures
* Multivariate limit theorems: limit distributions, central limit theorems, and related limit theorems
* Real-world applications
Limit Distributions for Sums of Independent Random Vectors is a comprehensive reference that provides an up-to-date survey of the state of the art in this important research area.

Recenzje

"Introduces the central limit theory of random vectors, an essential theory in probability and statistics, focusing on multivariate models." (SciTech Book News, Vol. 25, No. 3, September 2001)

"...well written with many insightful ideas...many interesting features...the most noteworthy being its coverage of limits. There are not many books at the same level." (Mathematical Reviews, 2002i)

"....a carefully written and accessible reference..." (Short Book Reviews, August 2002)

Spis treści

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.

O autorze

MARK M. MEERSCHAERT, PhD, is Associate Professor of Mathematics at the University of Nevada–Reno. He is also the author of Mathematical Modeling.

HANS–PETER SCHEFFLER, PhD, is Associate Professor of Mathematics at the University of Dortmund, Germany.