Limit Theorems of Probability Theory
Sequences of Independent Random Variables
Published on 27. April 1995
Book
Hardback
304 pages
978-0-19-853499-0 (ISBN)
Description
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.
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.
Reviews / Votes
It is a well-written scholarly work based on 487 references. Whilst reading the book one is amply rewarded by theory. Proceedings of the Edinburgh Mathematical Society 'In 1954 Gnedenko and Kolmogorov wrote a classic book on this subject. The present work is in the same spirit. ...It is a well-written scholarly work...this text should be a useful reference for a long time to come. * Proceedings of the Edinburgh Mathematical Society, 1996 * 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 worth will be appreciated by many in the years it will be of use.More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 21 mm
Weight
628 gr
ISBN-13
978-0-19-853499-0 (9780198534990)
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Schweitzer Classification
Person
Content
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 ; References ; Author index ; Subject index