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

Mark M. Meerschaert (Author), Hans-Peter Scheffler (Author)

9780471356295, Wiley

Hardback, published 27 July 2001

512 pages
24.8 x 16 x 2.9 cm, 0.905 kg

"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)

Die Quintessenz aus über 100 Originalarbeiten! Ausgehend von den Grundpfeilern der modernen Wahrscheinlichkeitstheorie entwickeln die Autoren dieses in sich geschlossenen, gut verständlich formulierten Bandes die Theorie der unendlich teilbaren Verteilungen und der regulären Variation. Im Anschluss erarbeiten sie die allgemeine Grenzwerttheorie für unabhängige Zufallsvektoren. Dabei achten sie sorgfältig darauf, alle Aspekte in den Kontext der Wahrscheinlichkeitslehre und Statistik zu stellen und bieten dafür eine Fülle von Zusatzinformationen an.

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.

Subject Areas: Mathematics [PB]