Characterization of Probability Distributions on Locally Compact Abelian Groups

✍ Scribed by Gennadiy Feldman

• Publisher: American Mathematical Society
• Year: 2023
• Tongue: English
• Leaves: 253
• Series: Mathematical Surveys and Monographs 273
• Category: Library

✦ Table of Contents

Contents
Preface
Chapter I. Preliminaries
1. Results of abstract harmonic analysis
2. Probability distributions on topological Abelian groups
3. Gaussian distributions on locally compact Abelian groups
Chapter II. Independent random variables with independent sum and difference
4. Identically distributed random variables
5. General case
Chapter III. Characterization of probability distributions through the independence of linear forms
6. General characterization theorems
7. Shifts of idempotent distributions on discrete and compact totally disconnected Abelian groups
8. Gaussian distributions on the cylinder ℝ×𝕋
Chapter IV. Characterization of probability distributions through the symmetry of the conditional distribution of one linear form given another
9. Locally compact Abelian groups containing no elements of order 2
10. Discrete and compact totally disconnected Abelian groups
11. Locally compact Abelian groups containing an element of order 2
Chapter V. Characterization theorems on the field of 𝑝-adic numbers
12. Skitovich–Darmois theorem
13. Heyde theorem
14. Characterization of shifts of idempotent distributions through the independence of sum and difference squared
Chapter VI. Miscellaneous characterization theorems
15. Rao theorems
16. Generalized Pólya theorem
Bibliography
Index of terms
Index of symbols