Quasi-linear PDEs and forward-backward stochastic differential equations: weak solutions

DOI10.1016/j.jde.2017.09.030OpenAlexW2760654024MaRDI QIDQ1680459

Huaizhong Zhao, Xince Wang, Chunrong Feng

Publication date: 16 November 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2017.09.030

zbMATH Keywords

ellipticweak solutionsparabolicforward-backward stochastic differential equationsprobabilistic representationquasi-linear partial differential equations

Mathematics Subject Classification ID

Ordinary differential equations (34-XX) Partial differential equations (35-XX)

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Cites Work

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• Probabilistic representation of weak solutions of partial differential equations with polynomial growth coefficients
• Adapted solution of a backward stochastic differential equation
• Probabilistic interpretation for a system of quasilinear parabolic partial differential equation combined with algebra equations
• Stochastic calculus with anticipating integrands
• Linear forward-backward stochastic differential equations
• Forward-backward stochastic differential equations and quasilinear parabolic PDEs
• Backward-forward stochastic differential equations
• Generalized solutions of a stochastic partial differential equation
• Backward doubly stochastic differential equations and systems of quasilinear SPDEs
• Solving forward-backward stochastic differential equations explicitly -- a four step scheme
• Perfect cocycles through stochastic differential equations
• Finding adapted solutions of forward-backward stochastic differential equations: Method of continuation
• A type of time-symmetric forward-backward stochastic differential equations
• On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case.
• Solution of forward-backward stochastic differential equations
• Stationary backward stochastic differential equations and associated partial differential equations
• Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients
• On well-posedness of forward-backward SDEs -- a unified approach
• SPDEs with polynomial growth coefficients and the Malliavin calculus method
• Stationary solutions of SPDEs and infinite horizon BDSDEs
• Sobolev Weak Solutions of the Hamilton--Jacobi--Bellman Equations
• Functional Integration and Partial Differential Equations. (AM-109)
• Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
• Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control
• Weak solutions for SPDE's and backward doubly stochastic differential equations
• Stochastic differential equations. An introduction with applications.