Approximation Methods in Probability Theory / by Vydas Čekanavičius.

Format:

Book

Author/Creator:

Čekanavičius, Vydas, Author.

Series:

Universitext, 0172-5939

Language:

English

Subjects (All):

Probabilities.

Approximation theory.

Probability Theory and Stochastic Processes.

Approximations and Expansions.

Local Subjects:

Probability Theory and Stochastic Processes.

Approximations and Expansions.

Physical Description:

1 online resource (XII, 274 p.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

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.

Contents:

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.

Notes:

Includes index.

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-34072-7

OCLC:

952413085