Decomposition of Multivariate Probabilities

Roger Cuppens, Z. W. Birnbaum, E. Lukacs

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780121994501
• eBook ISBN:
  9781483217642
• Topic: Mathématiques
• Subtopic: Mathématiques appliquées

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

• Front Cover
• Decomposition of Multivariate Probabilities
• Copyright Page
• Table of Contents
• Preface
• Notation
• List of Symbols
• Chapter 1. Measures and Integrals
• Chapter 2. Fourier-Stieltjes Transforms of Signed Measures
• Chapter 3. Analytic Characteristic Functions
• Chapter 4. Decomposition Theorems
• Chapter 5. Decomposition Theorems for Analytic Characteristic Functions
• Chapter 6. Infinitely Divisible Probabilities with Normal Factor
• Chapter 7. Infinitely Divisible Probabilities without Normal Factor
• Chapter 8. Infinitely Divisible Probabilities with Countable Poisson Spectrum
• Chapter 9. α-Decomposition
• Appendix A: Some Results of Function Theory
• Appendix B: Exponentials of Polynomials and Functions
• References
• Index