Approximation Methods in Probability Theory

Front Cover
Springer, Jun 16, 2016 - Mathematics - 274 pages

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.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

1 Definitions and Preliminary Facts
1
2 The Method of Convolutions
21
3 Local Lattice Estimates
50
4 Uniform Lattice Estimates
69
5 Total Variation of Lattice Measures
77
6 Nonuniform Estimates for Lattice Measures
93
7 Discrete Nonlattice Approximations
101
8 Absolutely Continuous Approximations
107
10 Lower Estimates
140
11 The Stein Method
153
12 The Triangle Function Method
179
13 Heinrichs Method for mDependent Variables
207
14 Other Methods
222
Solutions to Selected Problems
241
Index
273
Copyright

9 The Esseen Type Estimates
121

Other editions - View all

Common terms and phrases

About the author (2016)

Vydas Čekanavičius 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.

Bibliographic information