Diffusion approximation for random parabolic operators with oscillating coefficients

Marina Kleptsyna (1) , Andrey Piatnitski (2, 3) , Alexandre Popier (1)

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

We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variables and random stationary ergodic in time. As was proved in [24] and [12] in this case the homogenized operator is deterministic. The paper focuses on non-diffusive scaling, when the oscillation in spatial variables is faster than that in temporal variable. Our goal is to study the asymptotic behaviour of the normalized difference between solutions of the original and the homogenized problems.

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

Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier. Diffusion approximation for random parabolic operators with oscillating coefficients. 2017. ⟨hal-01419923v2⟩