Homogenization of random parabolic operators. Diffusion approximation.

Marina Kleptsyna (1) , Andrey Piatnitski (2) , Alexandre Popier (1)

1 LMM - Laboratoire Manceau de Mathématiques
2 LPI RAS - P. N. Lebedev Physical Institute of the Russian Academy of Sciences [Moscow]

The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in 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.

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier. Homogenization of random parabolic operators. Diffusion approximation.. 2013. ⟨hal-00842809v3⟩