Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients

2004/10/06 by Francois Delarue
Mathematics · #math.PR #msc:35B27 #msc:65C30 #msc:35K55

paper · pdf · doi:10.1214/009117904000000144

published as Annals of Probability 2004, Vol. 32, No. 3B, 2305-2361 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000144

arxiv created 2004/10/06 · arxiv updated 2009/12/01

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.''

Related

• Homogenization of semilinear parabolic PDEs with the third boundary conditions
• Periodic homogenization of a class of weakly coupled systems of linear PDEs
• Homogenization of Nonlocal Partial Differential Equations Related to Stochastic Differential Equations with Lévy Noise
• A CLT for degenerate diffusions with periodic coefficients, and\n application to homogenisation of linear PDEs
• Homogenization of semi-linear PDEs with discontinuous effective coefficients