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

Abstract : 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.
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Submitted on : Sunday, April 9, 2006 - 7:46:50 PM
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Antoine Lejay. A Probabilistic Approach to the Homogenization of Divergence-Form Operators in Periodic Media. Asymptotic Analysis, IOS Press, 2001, 28 (2), pp.151-162. ⟨inria-00001219⟩

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