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Monotone CFTP and coalescence time for Markov Processes

Le : 27/04/2009 11h00
Par : Pierre-Yves LOUIS (Université de Potsdam)
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Résumé : The Coupling-from-the-past (CFTP) technique for exact sampling from the steady state of a monotone ergodic Markov chain gives rise to the notion of complete monotonicity. We formalize and analyse the notions of stochastic monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which stochastic monotonicity and complete monotonicity coincide in continuous-time but not in discrete-time. The running time of the CFTP algorithm is the coalescence time. Its distribution will be discussed on some models.