Sums and Gaussian Vectors [electronic resource] / by Vadim Vladimirovich Yurinsky.

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.

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.