Sums and Gaussian Vectors

ISBN-13: 9783540603115 / Angielski / Miękka / 1995 / 312 str.

Vadim Yurinsky

Opis

This text surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Topics covered include probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, and estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces.

Spis treści

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.