Functional Equations in Probability Theory
eBook - PDF

Functional Equations in Probability Theory

  1. 268 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Functional Equations in Probability Theory

Book details
Table of contents
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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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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 & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2014
ISBN
9781483272221
Topic
Mathematics
Subtopic
Mathematical Analysis
Index
Mathematics

Table of contents

  1. Front Cover
  2. Functional Equations in Probability Theory
  3. Copyright Page
  4. Table of Contents
  5. Dedication
  6. Preface
  7. Introduction
  8. Chapter 1. Background Material
  9. Chapter 2. Integrated Cauchy Functional Equations on IR+
  10. Chapter 3. The Stable Laws, the Semistable Laws, and a Generalization
  11. Chapter 4. Integrated Cauchy Functional Equations with Error Terms on IR+
  12. Chapter 5. Independent/Identically Distributed Linear Forms, and the Normal Laws
  13. Chapter 6. Independent/Identical Distribution Problems Relating to Stochastic Integrals
  14. Chapter 7. Distribution Problems Relating to the Arc-sine, the Normal, and the Chi-Square Laws
  15. Chapter 8. Integrated Cauchy Functional Equations on IR
  16. Chapter 9. Integrated Cauchy Functional Equations on Semigroups of IRd
  17. Bibliography
  18. Index
  19. PROBABILITY AND MATHEMATICAL STATISTICS