Lectures on the Coupling Method

Torgny Lindvall

270 pages, parution le 01/09/2002

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Résumé

An important tool in probability theory and its applications, the coupling method is primarily used in estimates of total variation distances. The method also works well in establishing inequalities, and it has proven highly successful in the study of Markov and renewal process asymptotics. This text represents a detailed, comprehensive examination of the method and its broad variety of applications. Readers progress from simple to advanced topics, with end-of-discussion notes that reinforce the preceding material. Topics include renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. A practical and easy-to-use reference, this volume will accommodate the diverse needs of professionals in the fields of statistics, mathematics, and operational research, as well as those of teachers and students.

Contents

Introduction

Three Examples
An Outline
Notes

Preliminaries

What Is a Coupling?
The Coupling Inequality
Rates of Convergence
Weak Coupling
The gamma Coupling
The Polish Assumption
Notes

Discrete Theory

Renewal Theory
Markov Chains
Random Walk
Card Shuffling
Poisson Approximation

Continuous Theory

Renewal Theory
Harris Chains
Maximal Coupling
Regenerative Processes
On Markov Processes

Inequalities

Strassen's Theorem
Domination
Domination and Monotonicity of Markov Processes
Examples of Domination

Intensity-Governed Processes

Birth and Death Processes
General Birth and Death Processes
Interacting Particle Systems

Embedding in Poisson Processes

More Renewal Theory
On a Class of Point Processes

Diffusions

One-Dimensional Processes
Multidimensional Processes

Appendices

Polish Spaces
Epilogue

Caractéristiques techniques

	PAPIER
Éditeur(s)	Dover
Auteur(s)	Torgny Lindvall
Parution	01/09/2002
Nb. de pages	270
Format	13,6 x 21,3
Couverture	Broché
Poids	300g
Intérieur	Noir et Blanc
EAN13	9780486421452
ISBN13	978-0-486-42145-2