Realizable monotonicity for continuous-time Markov processes

Paolo Dai Pra (1) , Pierre-Yves Louis (2) , Ida Germana Minelli (1)

1 Dipartimento di Matematica Pura e Applicata [Padova]
2 Institut für Mathematik [Potsdam]

We formalize and analyze the notions of stochastic monotonicity and realizable mono-tonicity 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 realizable monotonicity coincide in continuous-time but not in discrete-time.

Mots clés: Markov processes; coupling; partial ordering; stochastic monotonicity; realizable monotonic-ity

Domaines: Probabilités [math.PR]

Paolo Dai Pra, Pierre-Yves Louis, Ida Germana Minelli. Realizable monotonicity for continuous-time Markov processes. Stochastic Processes and their Applications, 2010, 120 (6), pp.959--982. ⟨10.1016/j.spa.2010.03.002⟩. ⟨hal-01283792⟩