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Homogenization of random parabolic operators. Diffusion approximation

Author

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  • Kleptsyna, M.
  • Piatnitski, A.
  • Popier, A.

Abstract

This paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic with respect to the spatial variables and random stationary in time. Under proper mixing assumptions, we study the limit behaviour of the normalized difference between solutions of the original and the homogenized problems. The asymptotic behaviour of this difference depends crucially on the ratio between spatial and temporal scaling factors. Here we study the case of self-similar parabolic diffusion scaling.

Suggested Citation

  • Kleptsyna, M. & Piatnitski, A. & Popier, A., 2015. "Homogenization of random parabolic operators. Diffusion approximation," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1926-1944.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:5:p:1926-1944
    DOI: 10.1016/j.spa.2014.12.002
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    References listed on IDEAS

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    1. Campillo, Fabien & Kleptsyna, Marina & Piatnitski, Andrey, 2001. "Homogenization of random parabolic operator with large potential," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 57-85, May.
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