Coupling Methods in Probability Theory

Abstract

Coupling means the joint construction of two or more random elements (variables, processes), usually in order to deduce properties of the individual elements. In this paper the method is presented through a series of examples starting with correlation, domination and approximation of random variables, then turning to the asymptotics of Markov processes and random walks, and finally outlining recent developments in stochastic processes and Palm theory. The examples are picked for broadness and simplicity and all arguments are given in full detail (except in the survey part at the end).