Lectures on the Coupling MethodAn 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 | 1 |
Preliminaries | 9 |
Discrete Theory | 21 |
Continuous Theory | 67 |
Inequalities | 127 |
IntensityGoverned Processes | 151 |
Diffusions | 207 |
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Common terms and phrases
A₁ aperiodic asymptotics B₁ Basics birth and death bounded Brownian motion condition constant construction continuous-time convergence coupling inequality coupling method Cox processes death process decreasing defined denote diffusion Doeblin coupling E₁ equals ergodicity example exists finite follows Harris chain Hence i₁ illustrations implies independent initial distributions Lemma limsup Markov chain Markov kernel Markov process Markov property N₁ n₂ notation Notice o-field obtain P₁ partial ordering particle systems point process points of occurrence Poisson approximation Poisson process Polish Polish space positive recurrent probabilité probability measures probability space proof prove random elements random sequences random variables random walk Recall renewal process renewal theory result S₁ satisfying stationary distribution stochastically increasing successful coupling T₁ tion transition kernel V₁ W₁ weak coupling X₁ X₂ Y₁ Y₂ Z₁ zero-delayed
References to this book
Comparison Methods for Stochastic Models and Risks Alfred Müller,Dietrich Stoyan No preview available - 2002 |