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Monotonicity and complete monotonicity for continuous-time Markov chains. (English) Zbl 1098.60070

Summary: 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.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)

Software:

Scilab; GAP
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References:

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