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2022-12-19T04:15:12Z
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A Stochastic Representation for Fully Nonlinear PDEs and Its Application to Homogenization
Ichihara, Naoyuki
138714
415
Fully nonlinear parabolic equations
Hamilton-Jacobi-Bellman equations
backward stochastic differential equations
nonlinear Feynman-Kac formula
homogenization
application/pdf
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.
departmental bulletin paper
Graduate School of Mathematical Sciences, The University of Tokyo
2005-11-17
application/pdf
Journal of mathematical sciences, the University of Tokyo
3
12
467
492
AA11021653
13405705
https://repository.dl.itc.u-tokyo.ac.jp/record/40132/files/jms120306.pdf
eng