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Approximation Methods in Probability Theory

✍ Scribed by Vydas Čekanavičius (auth.)

Publisher
Springer
Year
2016
Tongue
English
Leaves
283
Series
Universitext
Edition
1
Category
Library
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✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Definitions and Preliminary Facts....Pages 1-20
The Method of Convolutions....Pages 21-49
Local Lattice Estimates....Pages 51-68
Uniform Lattice Estimates....Pages 69-76
Total Variation of Lattice Measures....Pages 77-92
Non-uniform Estimates for Lattice Measures....Pages 93-100
Discrete Non-lattice Approximations....Pages 101-106
Absolutely Continuous Approximations....Pages 107-120
The Esseen Type Estimates....Pages 121-139
Lower Estimates....Pages 141-152
The Stein Method....Pages 153-177
The Triangle Function Method....Pages 179-206
Heinrich’s Method for m-Dependent Variables....Pages 207-221
Other Methods....Pages 223-240
Back Matter....Pages 241-274

✦ Subjects

Probability Theory and Stochastic Processes; Approximations and Expansions

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