Comptes Rendus
Probability Theory
Monotonicity and complete monotonicity for continuous-time Markov chains
[Monotonie et monotonie complète des chaînes de Markov à temps continu]
Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 965-970.

Nous étudions les notions de monotonie et de monotonie complète pour les processus de Markov (ou chaînes de Markov à temps continu) prenant leurs valeurs dans un espace partiellement ordonné. Ces deux notions ne sont pas équivalentes, comme c'est le cas lorsque le temps est discret. Cependant, nous établissons que pour certains ensembles partiellement ordonnés, l'équivalence a lieu en temps continu bien que n'étant pas vraie en temps discret.

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.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2006.04.007

Paolo Dai Pra 1 ; Pierre-Yves Louis 2 ; Ida Minelli 1

1 Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy
2 Institut für Mathematik, Potsdam Universität, Am neuen Palais, 10 – Sans Souci, 14415 Potsdam, Germany
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     title = {Monotonicity and complete monotonicity for continuous-time {Markov} chains},
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Paolo Dai Pra; Pierre-Yves Louis; Ida Minelli. Monotonicity and complete monotonicity for continuous-time Markov chains. Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 965-970. doi : 10.1016/j.crma.2006.04.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.007/

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