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Stochastic comparisons for general probabilistic cellular automata

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  • López, F. Javier
  • Sanz, Gerardo

Abstract

In this work we study stochastic comparisons for probabilistic cellular automata where the set of values each automaton can take is an arbitrary finite set endowed with a partial or total order. We give necessary and sufficient conditions on the parameters which define the processes for their stochastic ordering. The equivalence is proved establishing the existence of increasing Markovian couplings of these processes. When such couplings exist, we give the explicit expression of their operators. As a consequence of these results, we get necessary and sufficient conditions on the transition probabilities of probabilistic cellular automata for their monotonicity.

Suggested Citation

  • López, F. Javier & Sanz, Gerardo, 2000. "Stochastic comparisons for general probabilistic cellular automata," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 401-410, February.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:4:p:401-410
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    References listed on IDEAS

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    1. 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.
    2. 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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    Cited by:

    1. Louis, P.-Y., 2005. "Increasing coupling of probabilistic cellular automata," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 1-13, August.

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    2. 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.

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