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Limit distributions for sums of independent random vectors : heavy tails in theory and practice

Author: Mark M Meerschaert; Hans-Peter Scheffler
Publisher: New York : Wiley, ©2001.
Series: Wiley series in probability and statistics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

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  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Mark M Meerschaert; Hans-Peter Scheffler
ISBN: 0471356298 9780471356295
OCLC Number: 46359950
Description: xiii, 484 pages : illustrations ; 25 cm.
Contents: Random Vectors --
Probability Distributions --
Convergence in Distribution --
Characteristic Functions --
Linear Operators --
Operator Norms --
Exponential Operators and Powers --
Convergence of Types --
Infinitely Divisible Distributions and Triangular Arrays --
Infinitely Divisible Distributions --
Convergence of Triangular Arrays --
Domains of Attraction --
Appendix: Continuous mappings into the circle --
Multivariate Regular Variation --
Regular Variation for Linear Operators --
Definitions and Basic Properties --
Uniform Convergence and Path Behavior --
The Spectral Decomposition --
Regular Variation for Real-Valued Functions --
Regularly Varying Functions --
Exponents and Symmetries --
Uniform Regular Variation --
Regular Variation for Borel Measures --
Regularly Varying Measures --
R-O Varying Measures --
Truncated Moments and Tail Moments --
Sharp Spectral Bounds --
Multivariate Limit Theorems --
The Limit Distributions --
Operator Semistable Laws --
Operator Stable Laws --
Stable Laws --
Semistable Laws --
Structure Theorems --
Central Limit Theorems --
Normal Limits --
Nonnormal Limits --
General Limits --
Stochastic Compactness --
Operator Stable Limits --
Related Limit Theorems --
Large Deviations --
Law of the Iterated Logarithm --
Convergence of Semitypes --
Applications --
Applications to Statistics --
Sample Moments --
Sample Covariance Matrix --
Self-Normalized Sums --
Tail and Moment Estimators --
Symmetric k-Tensors --
Time Series Analysis --
Self-Similar Stochastic Processes.
Series Title: Wiley series in probability and statistics.
Responsibility: Mark M. Meerschaert, Hans-Peter Scheffler.
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"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) Read more...

 
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