Approximation Methods in Probability Theory

This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems.

While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

Presents a unique collection of approximation methods in various metrics Explains the essential aspects of each method in detail Includes many exercises with solutions as well as bibliographical notes

Autorentext

Vydas ekanaviius is Professor of Statistics at Vilnius University. In 2005, he was co-winner of the Lithuanian State Award of Science for his research on compound approximations in probability theory. In his native country Lithuania, he is best known as the co-author of a best-selling three-volume textbook on statistics.

Inhalt
Definitions and preliminary facts.- The method of convolutions.- Local lattice estimates.- Uniform lattice estimates.- Total variation of lattice measures.- Non-uniform estimates for lattice measures.- Discrete non-lattice approximations.- Absolutely continuous approximations.- The Esseen type estimates.- Lower estimates.- The Stein method.- The triangle function method.- Heinrich's method for m-dependent variables.- Other methods.- Solutions to selected problems.- Bibliography.- Index.