Sasvári Multivariate Characteristic and Correlation Functions

1. Auflage 2013
ISBN: 978-3-11-022399-6
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 50, 375 Seiten, Gewicht: 10 g

Reihe: De Gruyter Studies in Mathematics

In a certain sense characteristic functions and correlation functions are the same, the common underlying concept is positive definiteness. Many results in probability theory, mathematical statistics and stochastic processes can be derived by using these functions. While there are books on characteristic functions of one variable, books devoting some sections to the multivariate case, and books treating the general case of locally compact groups, interestingly there is no book devoted entirely to the multidimensional case which is extremely important for applications. This book is intended to fill this gap at least partially. It makes the basic concepts and results on multivariate characteristic and correlation functions easily accessible to both students and researchers in a comprehensive manner.

The first chapter presents basic results and should be read carefully since it is essential for the understanding of the subsequent chapters. The second chapter is devoted to correlation functions, their applications to stationary processes and some connections to harmonic analysis. In Chapter 3 we deal with several special properties, Chapter 4 is devoted to the extension problem while Chapter 5 contains a few applications. A relatively large appendix comprises topics like infinite products, functional equations, special functions or compact operators.

Zielgruppe

Researchers, Lecturers, and Graduate Students in Mathematics; Academic Libraries

Autoren/Hrsg.

Sasvári, Zoltán

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Frontmatter
Preface
Contents
Chapter 1. Characteristic functions
Chapter 2. Correlation functions
Chapter 3. Special properties
Chapter 4. The extension problem
Chapter 5. Selected applications
Appendix A. Basic notation
Appendix B. Basic analysis
Appendix C. Advanced analysis
Appendix D. Functional analysis
Appendix E. Measure theory
Appendix F. Probability
Bibliography
Index

Über Autor(innen)

Sasvári, Zoltán
Zoltán Sasvári, Technische Universität Dresden.

Zoltán Sasvári, Technische Universität Dresden.