A Probabilistic Approach to the Homogenization of Divergence-Form Operators in Periodic Media
Lejay, Antoine
HAL, inria-00001219 / Harvested from HAL
Text on HAL
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.
Publié le : 2001-07-05
Classification:  divergence-form operators,  Dirichlet forms,  homogenization,  Feynman-Kac formula,  Girsanov Theorem,  AMS : 60H15 (35B27),  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{inria-00001219,
     author = {Lejay, Antoine},
     title = {A Probabilistic Approach to the Homogenization of Divergence-Form Operators in Periodic Media},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/inria-00001219}
}

Lejay, Antoine. A Probabilistic Approach to the Homogenization of Divergence-Form Operators in Periodic Media. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/inria-00001219/