- 262 pages
- English
- PDF
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Decomposition of Multivariate Probabilities
About This Book
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.
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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