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Uniform Limit Theorems for Sums of Independent Random Variables
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Proceedings of the Steklov Institute of Mathematics
1988; 222 pp; softcover
Volume: 174
Reprint/Revision History:
reprinted 1989
ISBN-10: 0-8218-3118-6
ISBN-13: 978-0-8218-3118-2
List Price: US$151 Member Price: US$120.80
Order Code: STEKLO/174

Among the diverse constructions studied in modern probability theory, the scheme for summation of independent random variables occupies a special place. In the study of even this comparatively simple scheme it is possible to become familiar with the fundamental regularities characterizing the cumulative influence of a large number of random factors. Further, this abstract model is useful in many important practical situations.

This book is devoted to the study of distributions of sums of independent random variables with minimal restrictions imposed on their distributions. The authors assume either that the distributions of the terms are concentrated on some finite interval to within a small mass, or that all the terms have the same, but arbitrary, distribution (or other conditions not connected with moment restrictions are introduced). Surprisingly, very substantive results are possible even under such a general statement of the problems.