Sums and Gaussian Vectors

Vadim Vladimirovich Yurinsky (auth.)3540603115, 9783540603115

Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.

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Table of contents :
Gaussian measures in euclidean space….Pages 1-42
Seminorms of Gaussian vectors in infinite dimensions….Pages 43-78
Inequalities for seminorms: Sums of independent random vectors….Pages 79-122
Rough asymptotics of large deviations….Pages 123-162
Gaussian and related approximations for distributions of sums….Pages 163-216
Fine asymptotics of moderate deviations….Pages 217-254