A stochastic representation for fully nonlinear PDEs and its application to homogenization
Vol. 12 (2005), No. 3, Page 467--492.
Ichihara, Naoyuki
A stochastic representation for fully nonlinear PDEs and its application to homogenization
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Abstract:
We establish a stochastic representation formula for solutions to fully nonlinear second-order partial differential equations of parabolic type. For this purpose, we introduce forward-backward stochastic differential equations with random coefficients. We next apply them to homogenization of fully nonlinear parabolic equations. As a byproduct, we obtain an estimate concerning the convergence rate of solutions. The results partially generalize homogenization of Hamilton-Jacobi-Bellman equations studied by R. Buckdahn and the author.
Keywords: Fully nonlinear parabolic equations, Hamilton-Jacobi-Bellman equations, backward stochastic differential equations, nonlinear Feynman-Kac formula, homogenization
Mathematics Subject Classification (2000): Primary 60H30; Secondary 35B27, 93E20.
Mathematical Reviews Number: MR2192225
Received: 2005-04-28
