Fourier Analysis in Probability Theory

✍ Scribed by Tatsuo Kawata, Z. W. Birnbaum and E. Lukacs (Auth.)

• Publisher: Elsevier Inc, Academic Press Inc
• Year: 1972
• Tongue: English
• Leaves: 673
• Series: Probability and mathematical statistics
• Category: Library

✦ Table of Contents

Content:
Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Page ii
Front Matter, Page iii
Copyright, Page iv
Preface, Pages xi-xii
I - Introduction, Pages 1-42
II - Fourier Series and Fourier Transforms, Pages 43-80
III - Fourier–Stieltjes Coefficients, Fourier–Stieltjes Transforms and Characteristic Functions, Pages 81-112
IV - Convergence and Summability Theorems, Pages 113-165
V - General Convergence Theorems, Pages 166-193
VI - L2-Theory of Fourier Series and Fourier Transforms, Pages 194-231
VII - Laplace and Mellin Transforms, Pages 232-277
VIII - More Theorems on Fourier and Laplace Transforms, Pages 278-329
IX - Convergence of Distribution Functions and Characteristic Functions, Pages 330-365
X - Some Properties of Characteristic Functions, Pages 366-399
XI - Distribution Functions and Their Characteristic Functions, Pages 400-474
XII - Convergence of Series of Independent Random Variables, Pages 475-535
XIII - Properties of Sums of Independent Random Variables; Convergence of Series in the Mean, Pages 536-604
XIV - Some Special Series of Random Variables, Pages 605-641
References, Pages 642-660
Index, Pages 661-668