This is a book on coupling, the method of establishing properties of random variables and processes (or any random things) through a joint construction on a common probability space. This is a general method relevant in all fields of probabilistic inquiry but the thrust is towards characterizations, approximations and asymptotics. The book also includes self-contained treatments of stationarity (Palm theory) and regeneration (classical, wide-sense, time-inhomogeneous, and taboo regeneration). Other topics discussed are ...
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This is a book on coupling, the method of establishing properties of random variables and processes (or any random things) through a joint construction on a common probability space. This is a general method relevant in all fields of probabilistic inquiry but the thrust is towards characterizations, approximations and asymptotics. The book also includes self-contained treatments of stationarity (Palm theory) and regeneration (classical, wide-sense, time-inhomogeneous, and taboo regeneration). Other topics discussed are perfect simulation (MCMC) and quasi-stationarity. Links are made to several fields such as quantum physics and non-locality, self-similarity, exchangeability, relativity, and queueing theory. The book is organized in chapters as follows: 1. Random Variables 2. Markov Chains and Random Walks 3. Random Elements 4. Stochastic Processes 5. Shift-Coupling 6. Markov Processes 7. Transformation Coupling 8. Stationarity, the Palm Dualities 9. The Palm Dualities in Higher Dimensions 10. Regeneration The book should be of interest to students and researchers in probability, stochastic modeling, and mathematical statistics. It is written with a Ph. even at an advanced undergraduate level. The book is self-contained, only relying on the measure theoretic basics and on elementary Markov chain theory. Hermann Thorisson received his Ph.
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Add this copy of Coupling, Stationarity, and Regeneration (Probability to cart. $226.43, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2000 by Springer.
