Monotonicity and complete monotonicity for continuous-time Markov chains
  We analyze the notions of 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 monotonicity and complete monotonicity coincide in continuous time but not in discrete-time. 
Paolo Dai Pra, Pierre-Yves Louis, Ida Minelli
math.PR