Áttunda málstofa haustsins verður föstudaginn 28. október kl 10:30 í Naustinu, húsi Endurmenntunar. Fyrirlesari er Hermann Þórisson, Háskóla Íslands. Titill hans er Forward and backward limits.
Abstract:
The main limit theorem of (time-homogeneous) Markov chains says that (under minimal conditions) a Markov chain tends to stationarity (equilibrium) as time tends to infinity. In 1938 Wolfgang Doeblin (1915-1940) presented a brilliant method to prove this result, the first example of the so-called coupling method. Doeblin’s idea went basically unnoticed until the 1970s but has since resulted in lively developments in probability theory. We shall outline a modern version of Doeblin’s proof.
We then note that the method can also be applied to time-inhomogeneous Markov chains. However, this does not lead to convergence to a limit, – or, rather, not without a change of perspective.