Decomposition of Multivariate Probabilities - 1st Edition - ISBN: 9780121994501, 9781483217642

Decomposition of Multivariate Probabilities

1st Edition

Authors: Roger Cuppens
Editors: Z. W. Birnbaum E. Lukacs
eBook ISBN: 9781483217642
Imprint: Academic Press
Published Date: 1st January 1975
Page Count: 262
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Description

Decomposition of Multivariate Probability is a nine-chapter text that focuses on the problem of multivariate characteristic functions.

After a brief introduction to some useful results on measures and integrals, this book goes on dealing with the classical theory and the Fourier-Stieltjes transforms of signed measures. The succeeding chapters explore the multivariate extension of the well-known Paley-Wiener theorem on functions that are entire of exponential type and square-integrable; the theory of infinitely divisible probabilities and the classical results of Hin?in; and the decompositions of analytic characteristic functions. Other chapters are devoted to the important problem of the description of a specific class on n-variate probabilities without indecomposable factors. The final chapter studies the problem of ?-decomposition of multivariate characteristic functions.

This book will prove useful to mathematicians and advance undergraduate and graduate students.

Table of Contents


Preface


Notation


List of Symbols


Chapter 1 Measures and Integrals


1.1 Measures


1.2 Integrals


1.3 Product Measures


1.4 Signed Measures


1.5 Singular and Absolutely Continuous Measures


1.6 Continuity Sets


Chapter 2 Fourier-Stieltjes Transforms of Signed Measures


2.1 Fourier-Stieltjes Transforms


2.2 Uniqueness Theorem


2.3 Inversion Formulas


2.4 Projection Theorem


2.5 Convolution Theorem


2.6 Continuity Theorems


2.7 Bochner's Theorem


2.8 A Characterization of the Fourier-Stieltjes Transform


2.9 Exponential of Signed Measures


Notes


Chapter 3 Analytic Characteristic Functions


3.1 Examples of Characteristic Functions


3.2 Derivatives of Characteristic Functions


3.3 Analytic Characteristic Functions


3.4 Some Characterization Theorems


3.5 An Extension of the Notion of Analytic Characteristic Functions


3.6 Convex Support of Signed Measures


Notes


Chapter 4 Decomposition Theorems


4.1 Indecomposable Probabilities


4.2 Infinitely Divisible Probabilities


4.3 Canonical Representations


4.4 A Limit Theorem


4.5 Hinčin's Theorem


4.6 Probabilities with No Indecomposable Factor


Notes


Chapter 5 Decomposition Theorems for Analytic Characteristic Functions


5.1 Decompositions of Derivable Characteristic Functions


5.2 Decompositions of Probabilities Belonging to Ar


5.3 Decompositions of Analytic Characteristic Functions


Notes


Chapter 6 Infinitely Divisible Probabilities with Normal Factor


6.1 Case n = 1


6.2 A Necessary Conditio

Details

No. of pages:
262
Language:
English
Copyright:
© Academic Press 1975
Published:
Imprint:
Academic Press
eBook ISBN:
9781483217642

About the Author

Roger Cuppens

About the Editor

Z. W. Birnbaum

E. Lukacs

Affiliations and Expertise

Bowling Green State University

Ratings and Reviews