Overview
- Provides an accessible introduction to asymptotic stochastics
- Includes 194 exercises with solutions
- Contains 138 self-questions to text comprehension while reading
Part of the book series: Mathematics Study Resources (MSR, volume 10)
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Keywords
- Limit Theorems of Probability Theory
- Asymptotic Statistics
- Understaning limit theorems of Statistics
- self-study
- U-statistics
- Donsker's Theorem
- Brownian Walk
- Methods of Moments
- Multivariate Central Limit Theorem
- Brownian Bridge
About this book
This textbook, which is based on the second edition of a book that has been previously published in German language, provides a comprehension-oriented introduction to asymptotic stochastics. It is aimed at the beginning of a master's degree course in mathematics and covers the material that can be taught in a four-hour lecture with two-hour exercises. Individual chapters are also suitable for seminars at the end of a bachelor's degree course.
In addition to more basic topics such as the method of moments in connection with the convergence in distribution or the multivariate central limit theorem and the delta method, the book covers limit theorems for U-statistics, the Wiener process and Donsker's theorem, as well as the Brownian bridge, with applications to statistics. It concludes with a central limit theorem for triangular arrays of Hilbert space-valued random elements with applications to weighted L² statistics.
The book is deliberately designed forself-study. It contains 138 self-questions, which are answered at the end of each chapter, as well as 194 exercises with solutions.
This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Authors and Affiliations
About the author
Norbert Henze is a retired professor of stochastics at the Karlsruhe Institute of Technology (KIT). He was awarded the Ars legendi Faculty Prize 2014 for excellent university teaching in mathematics.
Bibliographic Information
Book Title: Asymptotic Stochastics
Book Subtitle: An Introduction with a View towards Statistics
Authors: Norbert Henze
Series Title: Mathematics Study Resources
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2024
Softcover ISBN: 978-3-662-68922-6Due: 15 September 2024
eBook ISBN: 978-3-662-68923-3Due: 15 September 2024
Series ISSN: 2731-3824
Series E-ISSN: 2731-3832
Edition Number: 1
Number of Pages: XIV, 461
Number of Illustrations: 5 b/w illustrations, 23 illustrations in colour
Additional Information: English translation of the 2nd original German edition published by Springer-Verlag Heidelberg, 2024