Couplage monotone complet pour les processus de Markov
vendredi 9 décembre 2011, 14h30 - 15h30
This talk is based on a joint work with Paolo Dai Pra (Padua University) and Ida Minelli (L’Aquila, university).
We first recall the perfect simulation algorithm for Markov chains.
On combinatorial models, like tilings, monotonicity insures the efficency of these algorithms. We formalize and analyze the notions of stochastic monotonicity and complete monotonicity for Markov Chains valued in a finite partially ordered set.,in discrete-time and in continuous-time.
We characterize on the associated order-graph (Hasse diagram) when the equivalence betwwen the two notions holds. In particular, we show that there
are partially ordered sets for which stochastic monotonicity and realizable monotonicity coincide in continuous-time but not in discrete-time.