Description: During the last two decades, the coupling method has developed as a critically important tool in probability theory and its applications. Used primarily for estimates of total variation distances, the method also works well in establishing inequalities and has proven highly successful in the study of Markov and renewal process asymptotics. The range of applications, which now include queueing networks, epidemics and infinite particle systems, has rapidly grown. Yet, despite the acknowledged popularity and importance of the method, there existed no definitive reference on the coupling phenomenon. Until now. Lectures on the Coupling Method is the first detailed, comprehensive examination of the coupling method, its many uses, and gaining influence in probability studies. Designed as a premier introductory textbook, Lectures on the Coupling Method leads the reader from simple to advanced topics in a clear progressive format, while illustrating key facets of the method's underlying theory and mechanics. Complete with end-of-discussion notes, each chapter is a thorough and rigorous tutorial, designed to pique interest and strengthen subject mastery. Topics include: What is a coupling? the coupling inequality; renewal theory; the discrete renewal theorem; Markov chains; card shuffling; poisson approximation; Harris chains; ergodicity; maximal coupling; Markov processes; Strassen's theorem domination and monotonicity of Markov processes; and birth and death processes. The book also sheds light on the many special types of processes, such as random walks, diffusions, and regenerative processes, in which the method has proven useful. Complete with an explanatory list of notation used, subjectindex, ample references, and an appendix, the text is a practical, easy-to-use reference which accommodates the diverse informational needs of statistical, mathematical, operations research professionals, instructors, and students alike. A cornerstone textbook destined to serve as the field's common reference, Lectures on the Coupling Method is the first comprehensive look at the theory, features, and operational specifics central to the success of the coupling method.

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