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.
Author(s): Vadim Vladimirovich Yurinsky (auth.)
Series: Lecture Notes in Mathematics 1617
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1995
Language: English
Pages: 312
City: Berlin; New York
Tags: Probability Theory and Stochastic Processes; Statistical Physics
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
