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.

Bibliographic Information

Book Title: Sums and Gaussian Vectors
Authors: Vadim Vladimirovich Yurinsky
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0092599
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1995
Softcover ISBN: 978-3-540-60311-5Published: 17 November 1995
eBook ISBN: 978-3-540-44791-7Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 312
Topics: Probability Theory and Stochastic Processes, Complex Systems, Statistical Physics and Dynamical Systems

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Sums and Gaussian Vectors

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Table of contents (6 chapters)

Front Matter

Gaussian measures in euclidean space

Seminorms of Gaussian vectors in infinite dimensions

Inequalities for seminorms: Sums of independent random vectors

Rough asymptotics of large deviations

Gaussian and related approximations for distributions of sums

Fine asymptotics of moderate deviations

Back Matter

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