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Realizable monotonicity for continuous-time Markov processes

Author

Listed:
  • Dai Pra, Paolo
  • Louis, Pierre-Yves
  • Minelli, Ida Germana

Abstract

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

Suggested Citation

  • Dai Pra, Paolo & Louis, Pierre-Yves & Minelli, Ida Germana, 2010. "Realizable monotonicity for continuous-time Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 959-982, June.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:6:p:959-982
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    References listed on IDEAS

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    1. Louis, P.-Y., 2005. "Increasing coupling of probabilistic cellular automata," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 1-13, August.
    2. William A. Massey, 1987. "Stochastic Orderings for Markov Processes on Partially Ordered Spaces," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 350-367, May.
    3. Javier López, F. & Sanz, Gerardo, 1998. "Stochastic comparisons and couplings for interacting particle systems," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 93-102, September.
    4. Forbes, Florence & François, Olivier, 1997. "Stochastic comparison for Markov processes on a product of partially ordered sets," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 309-320, May.
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