Per Gösta Andersson: The Coupling Method: Two Simple Examples

Nowadays we often rely on computer simulations in order to achieve or illustrate asymptotic probabilistic or inferential results. Analytical approaches are often very difficult to use. Nevertheless, in this talk I will present and bring forward the coupling method. Two examples will be given to illustrate the main features of this probabilistic technique. In the first we will look at the asymptotic behaviour of a Markov chain and the second will deal with Poisson approximation.

The coupling method can be traced back to Wolfgang Doeblin (1915-1940). He is now recognized as one of the most brilliant mathematicians of the twentieth century. His work and short life with a very tragic ending during the Second World War would certainly qualify as a seminar of its own.