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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.
List of contents
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.
About the author
Mark M. Meerschaert is Chairperson of the Department of Statistics and Probability at Michigan State University and an Adjunct Professor in the Department of Physics at the University of Nevada. Professor Meerschaert has professional experience in the areas of probability, statistics, statistical physics, mathematical modeling, operations research, partial differential equations, ground water and surface water hydrology. He started his professional career in 1979 as a systems analyst at Vector Research, Inc. of Ann Arbor and Washington D.C., where he worked on a wide variety of modeling projects for government and industry. Meerschaert earned his doctorate in Mathematics from the University of Michigan in 1984. He has taught at the University of Michigan, Albion College, Michigan State University, the University of Nevada in Reno, and the University of Otago in Dunedin, New Zealand. His current research interests include limit theorems and parameter estimation for infinite variance probability models, heavy tail models in finance, modeling river flows with heavy tails and periodic covariance structure, anomalous diffusion, continuous time random walks, fractional derivatives and fractional partial differential equations, and ground water flow and transport.
Summary
This book provides an accessible, serious, and multivariate introduction to the central limit theorem of random variables that lies at the heart of probability and statistics. Practical applications of stable random variables are showcased.
Additional text
"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)
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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)
"...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)
