Coupling, Stationarity, And Regeneration

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.D. student in mind but the first two chapters can be read at master level and 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.D. from the Department of