This text represents a detailed, comprehensive examination of the coupling 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. 1992 edition.

Table of Contents for Lectures on the Coupling Method

	Introduction
	1. Three Examples
	2. An Outline
	3. Notes
Chapter I. Preliminaries
Appendix II
Bibliography
Index
	1. What Is a Coupling?
	2. The Coupling Inequality
	3. Rates of Convergence
	4. Weak Coupling
	5. The gamma Coupling
	6. The Polish Assumption
	7. Notes
Chapter II. Discrete Theory
	1. Renewal Theory
		1. Basics
		2. Stationarity. The Coupling
		3. The Discrete Renewal Theorem
		4. Finite Moments of T
		5. Renewal Sequences
		6. Notes
	2. Markov Chains
		7. Notation
		8. Positive Recurrent Chains
		9. Null-Recurrent Chains
		10. An Observation
		11. Notes
	3. Random Walk
		12. The Ornstein Coupling
		13. Null-Recurrent Markov Chains
		14. The Mineka Coupling
		15. Blocks
		16. The Harris Random Walk
		17. A Multidimensional Random Walk
		18. Notes
	4. Card Shuffling
		19. Basics
		20. "Top to Random" Shuffling
		21. Notes
	5. Poisson Approximation
		22. Basics
		23. Another Simple Coupling
		24. The Stein-Chen Method
		25. An Example
		26. Notes
Chapter III. Continuous Theory
	1. Renewal T
		2. Basics
		3. Stationarity
		4. Blackwell's Renewal Theorem
		4. Bounds for U
		5. An Exact Coupling
		6. Finite Moments of T. Rate Results
		7. Notes
	2. Harris Chains
		8. Basics
		9. Harris Chains
		10. Regeneration and Stationarity
		11. Ergodicity
		12. Random Walk
		13. Notes
	3. Maximal Coupling
		14. The Coupling. Goldstein's Theorem
		15. From Weak to Strong Coupling
		16. Notes
	4. Regenerative Processes
		17. Basics. Stationarity
		18. Coupling of Regenerative Processes
		19. Notes
	5. On Markov Processes
		20. Some Remarks
		21. Ergodicity
		22. Notes
Chapter IV. Inequalities
	1. Strassen's Theorem
		1. Basics
		2. The Theorem
		3. Alternative Formulations
		4. Notes
	2. Domination
		5. The General Result
		6. Monotonicity and Convergence
		7. Notes
	3. Domination and Monotonicity of Markov Processes
		8. Basics
		9. A Monotonicity Result
	4. Examples of Domination
		10. Direct Constructions
		11. Percolation
		12. Bernstein Polynomials
		13. Increasing Power Func
		14. Cox Processes
		15. Notes
Chapter V. Intensity-Governed Processes
	1. Birth and Death Processes
		1. Basics
		2. Ergodicity
		3. Rates
		4. Domination and Monotonicity
		5. Notes
	2. General Birth and Death Processes
		6. Basics
		7. Ergodicity
		8. Networks
		9. Propagations
		10. Notes
	3. Interacting Particle Systems
		11. A Signpost. Basics and Examples
		12. The Vasershtein Coupling
		13. Attractiveness and Monotonicity
		14. On the Example Processes
		15. Notes
	4. Embedding in Poisson Processes
		16. A Multivariate Exponential Distribution
		17. Embedding in a Bivariate Poisson Process
		18. Urns and Boxes
		19. On Free Parking Spaces
		20. Notes
	5. More Renewal Theory
		21. Basics
		22. The DFR Case
		23. The IFR Case
		24. Notes
	6. On a Class of Point Processes
		25. Basics
		26. On the FDR Concept
		27. The (A, m) Processes
		28. Notes
Chapter VI. Diffusions
	1. One-Dimensional Processes
		1. Basics
		2. Ergodicity. I Closed
		3. Ergodicity. I Not Closed
		4. The Strong Feller Property
		5. Domin
		6. Notes
	2. Multidimensional Processes
		7. Basics
		8. Brownian Motion
		9. Radial Drift
		10. Another Reflection Coupling
		11. Notes
Appendix 1. Polish Spaces
	Appendix 1. A Quick survey
	Appendix 2. The Banach space bM subscript s
	Appendix 3. Notes
	Appendix 4. Epilogue
Appendix 5. Some History
Frequently Used Notation; References; Index

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