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Propriété de Markov des équations stationnaires discrètes quasi-linéaires

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  • Donati-Martin, C.

Abstract

In this paper, we consider the stochastic discrete equation - [Delta]U(x)+[latin small letter f with hook](U(x))=A(x) where x runs over a finite domain [Theta] of , [Delta] is a discretization od the Laplacian operator, {A(x)} is a sequence of i.i.d. Gaussian variables, and we impose the Dirchlet condition U(x)=0 for x[negated set membership][Theta]. We prove existence and uniquesness of a solution assuming monotonicity condition on [latin small letter f with hook], and we study the Markov property of the solution.

Suggested Citation

  • Donati-Martin, C., 1993. "Propriété de Markov des équations stationnaires discrètes quasi-linéaires," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 61-84, October.
    • Handle: RePEc:eee:spapps:v:48:y:1993:i:1:p:61-84
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    Cited by:

    1. Baccin, Maria C. & Ferrante, Marco, 1995. "On a stochastic delay difference equation with boundary conditions and its Markov property," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 131-146, November.

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