Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients.

DOI10.1214/009117904000000144zbMath1073.35021arXivmath/0410163OpenAlexW3101504230MaRDI QIDQ1889783

François Delarue

Publication date: 10 December 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410163

zbMATH Keywords

forward-backward stochastic equationssystem of quasilinear PDEs

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Nonlinear parabolic equations (35K55) Applications of stochastic analysis (to PDEs, etc.) (60H30) PDEs with randomness, stochastic partial differential equations (35R60) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Stochastic integral equations (60H20)

Related Items (12)

HOMOGENIZATION OF A PERIODIC DEGENERATE SEMILINEAR ELLIPTIC PDE ⋮ Reflected BSDE and Locally Periodic Homogenization of Semilinear PDEs with Nonlinear Neumann Boundary Condition ⋮ Weak existence and uniqueness for forward-backward SDEs ⋮ Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs ⋮ Homogenization of periodic semilinear hypoelliptic PDEs ⋮ Averaging for BSDEs with null recurrent fast component. Application to homogenization in a non periodic media ⋮ Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach ⋮ A forward-backward stochastic algorithm for quasi-linear PDEs ⋮ Fluctuations of Random Semilinear Advection Equations ⋮ Homogenization of periodic semilinear parabolic degenerate PDEs ⋮ An averaging principle for nonlinear parabolic PDEs via FBSDEs driven by \(G\)-Brownian motion ⋮ Approximation of a degenerate semilinear PDE with a nonlinear Neumann boundary condition

Cites Work

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• Adapted solution of a backward stochastic differential equation
• Tightness criteria for laws of semimartingales
• Forward-backward stochastic differential equations and their applications
• Forward-backward stochastic differential equations and quasilinear parabolic PDEs
• Solving forward-backward stochastic differential equations explicitly -- a four step scheme
• A non-Skorokhod topology on the Skorokhod space
• On Poisson equation and diffusion approximation. II.
• BSDE driven by Dirichlet process and semi-linear parabolic PDE. Application to homogeniza\-tion.
• On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case.
• Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: A probabilistic approach
• On the Poisson equation and diffusion approximation. I
• Probabilistic approach to homogenization of viscosity solutions of parabolic PDEs
• Compactness methods in the theory of homogenization II: Equations in non-divergence form
• SOME NEW RESULTS IN THE THEORY OF CONTROLLED DIFFUSION PROCESSES
• Probabilistic approach to singular perturbations of semilinear and quasilinear parabolic PDEs
• Probabilistic approach to homogenizations of systems of quasilinear parabolic PDEs with periodic structures
• Averaging of backward stochastic differential equations, with application to semi-linear pde's
• The perturbed test function method for viscosity solutions of nonlinear PDE
• Bounds for the fundamental solution of a parabolic equation
• BSDEs, convergence in law and homogenization of semilinear parabolic SDEs
• Homogenization of random semilinear PDEs

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