Asymptotic Stochastics
An Introduction with a View towards Statistics
Springer Berlin Heidelberg
ISBN 978-3-662-68923-3
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Bibliografische Daten
eBook. PDF
2024
XIX, 467 p..
In englischer Sprache
Umfang: 467 S.
Verlag: Springer Berlin Heidelberg
ISBN: 978-3-662-68923-3
Weiterführende bibliografische Daten
Das Werk ist Teil der Reihe: Mathematics Study Resources
Produktbeschreibung
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 for self-study. It contains 138 self-questions, which are answered at the end of each chapter, as well as 194 exercises with solutions.
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.
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