Limit Theorems of Probability Theory: Sequences of Independent Random Variables

ISBN : 9780198534990

Valentin V. Petrov
304 Pages
161 x 241 mm
Pub date
Apr 1995
Oxford Studies in Probability
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This book is devoted to limit theorems and probability inequalities for sums of independent random variables. It includes 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 also many inequalities for sums of an arbitrary number of random variables. The aim of the book is two-fold. First, the book can be a basis for a course in probability for graduate or advanced undergraduate students. Second, the book can serve as a reference formulations of many (mostly recent) results which are usually inaccessible in book form. These supplements border on the basic text and make it possible for the reader to look at the frontier of modern investigations.


Notations and abbreviations
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
Author index
Subject index

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