Multivariate characteristic and correlation functions / Zoltán Sasvári.

Format:

Book

Author/Creator:

Sasvári, Zoltán.

Series:

De Gruyter Studies in Mathematics

De Gruyter Studies in Mathematics ; 50

Language:

English

Subjects (All):

Characteristic functions.

Correlation (Statistics).

Variables (Mathematics).

Multivariate analysis.

Physical Description:

1 online resource (376 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, 2013.

Language Note:

English

Summary:

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.

Contents:

Front matter

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

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [357]-360) and index.

ISBN:

9783110223996

3110223996

OCLC:

851970517