An averaging principle for nonlinear parabolic PDEs via FBSDEs driven by \(G\)-Brownian motion

DOI10.1016/j.jmaa.2021.125893zbMath1490.60187OpenAlexW4200283124MaRDI QIDQ2069922

Falei Wang, Ming Shang Hu, Lianzi Jiang

Publication date: 21 January 2022

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2021.125893

zbMATH Keywords

backward stochastic differential equationaveraging principle\(G\)-Brownian motionfully nonlinear PDE

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Nonlinear processes (e.g., (G)-Brownian motion, (G)-Lévy processes) (60G65)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Wellposedness of second order backward SDEs
• Average and deviation for slow-fast stochastic partial differential equations
• Averaging for BSDEs with null recurrent fast component. Application to homogenization in a non periodic media
• Martingale representation theorem for the \(G\)-expectation
• Gradient estimates for nonlinear diffusion semigroups by coupling methods
• Limit theorem for controlled backward SDEs and homogenization of Hamilton-Jacobi-Bellman equations
• Averaging principle for a class of stochastic reaction-diffusion equations
• Reflected solutions of backward SDE's, and related obstacle problems for PDE's
• Singular perturbations of nonlinear degenerate parabolic pDEs: A general convergence result
• Stochastic control for a class of nonlinear kernels and applications
• On the Poisson equation and diffusion approximation. I
• Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients.
• Probabilistic approach to homogenization of viscosity solutions of parabolic PDEs
• Properties of \(G\)-martingales with finite variation and the application to \(G\)-Sobolev spaces
• An efficient numerical method for forward-backward stochastic differential equations driven by \(G\)-Brownian motion
• Backward stochastic differential equations driven by \(G\)-Brownian motion with uniformly continuous generators
• Second order backward SDE with random terminal time
• Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs
• Robust mean-variance hedging via \(G\)-expectation
• Backward stochastic differential equations driven by \(G\)-Brownian motion
• Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by \(G\)-Brownian motion
• Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation
• Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs
• User’s guide to viscosity solutions of second order partial differential equations
• Probabilistic approach to homogenizations of systems of quasilinear parabolic PDEs with periodic structures
• Averaging Principle for Nonautonomous Slow-Fast Systems of Stochastic Reaction-Diffusion Equations: The Almost Periodic Case
• Nonlinear Expectations and Stochastic Calculus under Uncertainty
• Averaging of Backward Stochastic Differential Equations and Homogenization of Partial Differential Equations with Periodic Coefficients

This page was built for publication: An averaging principle for nonlinear parabolic PDEs via FBSDEs driven by \(G\)-Brownian motion