Sums and Gaussian Vectors

1995
ISBN: 978-3-540-60311-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1617, 312 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1010 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Yurinsky, Vadim

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

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.