Department of Mathematics

Prof. David McDonald, Ottawa University, Kanada: "Yaglom limits for $R$-transient chains with non-trivial Martin boundary"

Jun 06, 2018 from 04:15 PM to 05:15 PM

LMS 4 - Raum 424 - Kleiner Hörsaal

Abstract:

To quote John Maynard Keynes,"The long run is a misleading guide to current affairs. In the long run we are all dead". Keynes means it may be more useful to study the transient or quasi-stationary behaviour of an economic system instead of steady state. The study of quasi-stationary behaviour of an absorbing Markov chain was initiated by Yaglom who gave the limiting conditional behavior given non-absorption.

Here we construct a simple example of an absorbing Markov chain on a countable state space S.  The transition matrix K on S is irreducible and strictly substochastic. We determine the Yaglom limit, that is, the limiting conditional behavior given non-absorption.  Each starting state x in S results in a different Yaglom limit and each Yaglom limit is a quasi-stationary distribution.  We give an intuitive idea of why Yaglom limits can  depend on the initial distribution.

 

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