Jacka, Saul; Warren, John Examples of convergence and non-convergence of Markov chains conditioned not to die. (English) Zbl 1014.60074 Electron. J. Probab. 7, Paper No. 1, 22 p. (2002). Authors’ abstract: The authors give two examples of evanescent Markov chains which exhibit unusual behavior on conditioning to survive for large times. In the first example they 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. Reviewer: Uwe Rösler (Kiel) Cited in 2 Documents MSC: 60J50 Boundary theory for Markov processes 60B10 Convergence of probability measures 60G99 Stochastic processes 60J27 Continuous-time Markov processes on discrete state spaces 60J45 Probabilistic potential theory 60J55 Local time and additive functionals Keywords:conditioned Markov process; evanescent process; Martin boundary; Martin topology; superharmonic function; Choquet representation; Kolmogorov K2 chain; Skorokhod topology PDFBibTeX XMLCite \textit{S. Jacka} and \textit{J. Warren}, Electron. J. Probab. 7, Paper No. 1, 22 p. (2002; Zbl 1014.60074) Full Text: DOI EuDML EMIS