Examples of Convergence and Non-convergence of Markov Chains Conditioned Not To Die

Saul Jacka (University of Warwick)
Jon Warren (University of Warwick)

Abstract


In this paper we give two examples of evanescent Markov chains which exhibit unusual behaviour on conditioning to survive for large times. In the first example we show that the conditioned processes converge vaguely in the discrete topology to a limit with a finite lifetime, but converge weakly in the Martin topology to a non-Markovian limit. In the second example, although the family of conditioned laws are tight in the Martin topology, they possess multiple limit points so that weak convergence fails altogether.

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Pages: 1-22

Publication Date: October 3, 2001

DOI: 10.1214/EJP.v7-100

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