Sums and Gaussian Vectors [electronic resource] / by Vadim Vladimirovich Yurinsky.
Material type: TextSeries: Lecture Notes in Mathematics ; 1617Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1995Description: XII, 312 p. online resourceContent type:- text
- computer
- online resource
- 9783540447917
- 519.2 23
- QA273.A1-274.9
- QA274-274.9
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.
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