A Probabilistic Approach to the Homogenization of Divergence-Form Operators in Periodic Media

Antoine Lejay (1, 2)

1 SYSDYS - Stochastic Dynamical Systems
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We prove here using stochastic analysis the homogenization property of second-order divergence-form operators with lower-order differential terms (possibly highly-oscillating) in periodic media. The coefficients are not assumed to have any regularity, so the stochastic calculus theory for processes associated to Dirichlet forms is used. The Girsanov Theorem and the Feynman-Kac formula are used to work on the probabilistic representation of the solutions of some PDEs.

Mots clés: divergence-form operators; Dirichlet forms; homogenization; Feynman-Kac formula; Girsanov Theorem

Domaines: Probabilités [math.PR]

Antoine Lejay. A Probabilistic Approach to the Homogenization of Divergence-Form Operators in Periodic Media. Asymptotic Analysis, 2001, 28 (2), pp.151-162. ⟨inria-00001219⟩