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On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to ∇ϕ interface model
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  • Published: 03 May 2005

On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to ∇ϕ interface model

  • T. Delmotte1 &
  • J.-D. Deuschel2 

Probability Theory and Related Fields volume 133, pages 358–390 (2005)Cite this article

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Abstract.

We consider diffusions on ℝd or random walks on ℤd in a random environment which is stationary in space and in time and with symmetric and uniformly elliptic coefficients. We show existence and Hölder continuity of second space derivatives and time derivatives for the annealed kernels of such diffusions and give estimates for these derivatives. In the case of random walks, these estimates are applied to the Ginzburg-Landau ∇ϕ interface model.

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Authors and Affiliations

  1. Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex 4, France

    T. Delmotte

  2. TU Berlin, Fak. II Mathematik/Naturwissenschaften, Institut für Mathematik, Straße des 17. Juni 136, 10623, Berlin, Deutschland

    J.-D. Deuschel

Authors
  1. T. Delmotte
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  2. J.-D. Deuschel
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Correspondence to T. Delmotte.

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Delmotte, T., Deuschel, JD. On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to ∇ϕ interface model. Probab. Theory Relat. Fields 133, 358–390 (2005). https://doi.org/10.1007/s00440-005-0430-y

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  • Received: 07 November 2002

  • Revised: 04 January 2005

  • Published: 03 May 2005

  • Issue Date: November 2005

  • DOI: https://doi.org/10.1007/s00440-005-0430-y

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Keywords

  • Stochastic Process
  • Probability Theory
  • Time Derivative
  • Mathematical Biology
  • Random Environment
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