Limit Theorems of Probability Theory: Sequences of Independent Random Variables

Hardcover | April 1, 1995

byValentin V. PetrovAs told byV. V. Petrov

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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 lawof 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 supplementsborder on the basic text and make it possible for the reader to look at the frontier of modern investigations.

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From the Publisher

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 lawof the iterated logarithm, and also many in...

Valentin V. Petrov is at St Petersburg University, St Petersburg.

other books by Valentin V. Petrov

Sums of Independent Random Variables
Sums of Independent Random Variables

Paperback|Oct 22 2011

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Format:HardcoverDimensions:304 pages, 9.17 × 6.3 × 0.91 inPublished:April 1, 1995Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:019853499X

ISBN - 13:9780198534990

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Table of Contents

Notations and abbreviations1. Some basic concepts and theorems of probability theory2. Probability inequalities for sums of independent random variables3. Weak limit-theorems: convergence to infinitely divisible distributions4. Weak limit-theorems: the central limit theorem and the weak law of large numbers5. Rates of convergence in the central limit theorem6. Strong limit theorems: the strong law of large numbers7. Strong limit theorems: the law of the iterated logarithmReferencesAuthor indexSubject index

Editorial Reviews

Each chapter has a concise account of the core theory, with proofs but with full bibliographic information. The Addenda are a remarkable achievement and give the book its real added value over the competition...Professor Petrov has again given us what will become a standard work and its worthwill be appreciated by many in the years it will be of use.