|Coupling, Stationarity, and Regeneration
This book is an excellent self-contained exposition of the theory of coupling and its applications.
Alexander V.Bulinski , Zentralblatt MATH, 2000
"Coupling, Stationarity, and Regeneration" is an extraordinary and magnificient achievement that will have lasting impact on the world of probability.
Andrew D. Barbour, Journal of the American Statistical Association
Title: Coupling, Stationarity, and Regeneration
Author: Hermann Thorisson
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From the back-cover-text:
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. Coupling is
a general method relevant in all fields of probabilistic inquiry; how-
ever the main thrust is towards characterizations, approximations,
asymptotics, and simulation.
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 nonlocality,
self-similarity, exchangeability, relativity, and queueing theory.
The book is organized in chapters as follows:
The book should be of interest to students and researchers in
probability, stochastic modelling, and mathematical statistics. It
is written with a Ph.D. student in mind, and the first two chapters
can be read at the master's level and even at an advanced under-
graduate level. The book is mathematically self-contained, relying
only on the measure-theoretic basics and on elementary Markov
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