Limit Theorems of Probability Theory Sequences of Independent Random Variables [Hardcover]

This book offers a superb overview of limit theorems and probability inequalities for sums of independent random variables. Unique in its combination of both classic and recent results, the book details the many practical aspects of these important tools for solving a great variety of problems in probability and statistics. Topics include limit theorems on convergence to infinitely divisible distributions, the central limit theorem with rates of convergence, the weak and strong law of large numbers, the law of the iterated logarithm, and the many inequalities for sums of an arbitrary number random variables. Ideal as both a graduate text and a reference for seasoned mathematicians,Limit Theorems of Probability Theorybrings the reader to the frontier of current research.

1. Some Basic Concepts and Theorems of Probability Theory
2. Probability Inequalities for Sums of Independent Random Variables
3. Weak Limit Theorems: Convergence to Infinitely Divisible Distributions
4. Weak Limit Theorems: The Central Limit Theorem and the Weak Law of Large Numbers
5. Rates of Convergence in the Central Limit Theorem
6. Strong Limit Theorems: The Strong Law of Large Numbers
7. Strong Limit Theorems: The Law of the Iterated Logarithm
References
Author index
Subject index

The present book covers classical results as well as several new methods developed after 1975 . . . . All probabilists will find something interesting and/or useful . . . . The results and the proofs are clearly presented. The exposition in the basic sections of the book is self-contained, with detailed proofs. Hence, the book is suitable for a course on limit theorems for graduate students. The book can also serve as a reference book for researchers in probability theory and theoretical statistics. --Mathematical Reviews

Can be used as a basis for a course in probability theory for graduate or advanced undergraduate students...[and] as a rel£¡