# coupling methods in probability theory

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Applications in regeneration, Markov theory, Palm theory, ergodic theory, exchangeability and self-similarity are indicated and a set of general coupling references provided. Supplementary Studies 2. Includes new coverage on coupling methods, renewal theory, queueing theory, and a new derivation of Poisson process; Offers updated examples and exercises throughout, along with required material for Exam 3 of the Society of Actuaries The coupling method has long been an important tool in probability theory, see e.g. rev 2020.11.24.38066, The best answers are voted up and rise to the top, MathOverflow works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Nice examples/arguments that illustrating the coupling method in probability theory, http://blameitontheanalyst.wordpress.com/2012/01/24/probabilistic-coupling/, “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…, Regular Conditional Probability given a natural filtration of a stochastic process, Defining measures over frames in place of $\sigma$-algebras, Birkhoff Ergodic Theorem and Ergodic Decomposition Theorem for Continuous-Time Markov Processes, Stationary distribution of last passage percolation. Unable to display preview. Imagine a infinite ladder with rungs labelled by the positive integers. One of the deepest and most beautiful coupling arguments I have seen is the proof by Moser and Tardos of their Algorithmic Local Lemma. Proof of the convergence to stationary measure in Markov chain theory, this is now the "classical" way followed by most text books. They were introduced by Doeblin ([29]) in the thirties, the reader will find a survey and a sketch of the history in [54]. Coupling methods for Markov processes. MathOverflow is a question and answer site for professional mathematicians. COUPLING METHODS IN PROBABILITY in Ellös, Sweden, June 14-19, 1999 The development in the last few decades of the coupling method in pure and applied probability has been remarkable. Probability and Random Processes. ; Teen mothers who live with their parents are less likely to use marijuana than teen moms in other living arrangements. Their proof uses a coupling argument: before resampling any variables, you choose an infinite table of values for all variables, listing all the future resamplings. The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. ; He won the lottery! Asking for help, clarification, or responding to other answers. This is a preview of subscription content, https://doi.org/10.1007/978-1-4612-2224-8_19. I'll suggest "Coupling, stationarity, and regeneration" by Hermann Thorisson. Let $X_n$ be a Binomial random variable with probability $p$ and $n$ trials. Dynkin's card trick. Coupling methods have applications in many areas of probability theory. Description. The course is about the method of coupling in probability and its use in Monte Carlo methods, which refer to algorithms generating samples from probability distributions of interest. pp 319-339 | On the other hand if you are looking for original results proved using coupling arguments then have a look at: http://arxiv.org/abs/math/0404356.