- 271 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Functional Equations in Probability Theory
About this book
Functional Equations in Probability Theory deals with functional equations in probability theory and covers topics ranging from the integrated Cauchy functional equation (ICFE) to stable and semistable laws. The problem of identical distribution of two linear forms in independent and identically distributed random variables is also considered, with particular reference to the context of the common distribution of these random variables being normal. Comprised of nine chapters, this volume begins with an introduction to Cauchy functional equations as well as distribution functions and characteristic functions. The discussion then turns to the nonnegative solutions of ICFE on R+; ICFE with a signed measure; and application of ICFE to the characterization of probability distributions. Subsequent chapters focus on stable and semistable laws; ICFE with error terms on R+; independent/identically distributed linear forms and the normal laws; and distribution problems relating to the arc-sine, the normal, and the chi-square laws. The final chapter is devoted to ICFE on semigroups of Rd. This book should be of interest to mathematicians and statisticians.
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Table of contents
- Front Cover
- Functional Equations in Probability Theory
- Copyright Page
- Table of Contents
- Dedication
- Preface
- Introduction
- Chapter 1. Background Material
- Chapter 2. Integrated Cauchy Functional Equations on IR+
- Chapter 3. The Stable Laws, the Semistable Laws, and a Generalization
- Chapter 4. Integrated Cauchy Functional Equations with Error Terms on IR+
- Chapter 5. Independent/Identically Distributed Linear Forms, and the Normal Laws
- Chapter 6. Independent/Identical Distribution Problems Relating to Stochastic Integrals
- Chapter 7. Distribution Problems Relating to the Arc-sine, the Normal, and the Chi-Square Laws
- Chapter 8. Integrated Cauchy Functional Equations on IR
- Chapter 9. Integrated Cauchy Functional Equations on Semigroups of IRd
- Bibliography
- Index
- PROBABILITY AND MATHEMATICAL STATISTICS
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Yes, you can access Functional Equations in Probability Theory by Ramachandran Balasubrahmanyan,Ka-Sing Lau in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.