Author	Yurinsky, Vadim Vladimirovich. author
Title	Sums and Gaussian Vectors [electronic resource] / by Vadim Vladimirovich Yurinsky
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1995
Connect to	http://dx.doi.org/10.1007/BFb0092599
Descript	XII, 312 p. online resource

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

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

1. Mathematics
2. Probabilities
3. Statistical physics
4. Dynamical systems
5. Mathematics
6. Probability Theory and Stochastic Processes
7. Statistical Physics
8. Dynamical Systems and Complexity