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Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients

Francois Delarue
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Abstract

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the theory of forward-backward stochastic differential equations and introduce the new concept of ``auxiliary SDEs.''

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Francois Delarue. 2004-10-06. Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients. https://doi.org/10.1214/009117904000000144

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