Limit Theorems of Probability Theory

✍ Scribed by V. V. Petrov (auth.), Yu. V. Prokhorov, V. Statulevičius (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2000
• Tongue: English
• Leaves: 279
• Edition: 1
• Category: Library

✦ Synopsis

This book consists of five parts written by different authors devoted to various problems dealing with probability limit theorems. The first part, "Classical-Type Limit Theorems for Sums ofIndependent Random Variables" (V.v. Petrov), presents a number of classical limit theorems for sums of independent random variables as well as newer related results. The presentation dwells on three basic topics: the central limit theorem, laws of large numbers and the law of the iterated logarithm for sequences of real-valued random variables. The second part, "The Accuracy of Gaussian Approximation in Banach Spaces" (V. Bentkus, F. G6tze, V. Paulauskas and A. Rackauskas), reviews various results and methods used to estimate the convergence rate in the central limit theorem and to construct asymptotic expansions in infinite-dimensional spaces. The authors con­ fine themselves to independent and identically distributed random variables. They do not strive to be exhaustive or to obtain the most general results; their aim is merely to point out the differences from the finite-dimensional case and to explain certain new phenomena related to the more complex structure of Banach spaces. Also reflected here is the growing tendency in recent years to apply results obtained for Banach spaces to asymptotic problems of statistics.

✦ Table of Contents

Front Matter....Pages I-X
Classical-Type Limit Theorems for Sums of Independent Random Variables....Pages 1-24
The Accuracy of Gaussian Approximation in Banach Spaces....Pages 25-111
Approximation of Distributions of Sums of Weakly Dependent Random Variables by the Normal Distribution....Pages 113-165
Refinements of the Central Limit Theorem for Homogeneous Markov Chains....Pages 167-183
Limit Theorems on Large Deviations....Pages 185-266
Back Matter....Pages 267-275

✦ Subjects

Probability Theory and Stochastic Processes