Sobolev weak solutions for parabolic PDEs and FBSDEs

DOI10.1016/j.crma.2009.03.002zbMath1177.35117OpenAlexW1972523482MaRDI QIDQ1018123

Feng Zhang

Publication date: 13 May 2009

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2009.03.002

zbMATH Keywords

monotone coefficientsforward backward stochastic differential equationquasilinear parabolic PDEs

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs with randomness, stochastic partial differential equations (35R60) Initial value problems for second-order parabolic equations (35K15)

Cites Work

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• Backward-forward stochastic differential equations
• Dynamic Programming Principle for One Kind of Stochastic Recursive Optimal Control Problem and Hamilton–Jacobi–Bellman Equation
• Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
• Weak Solutions of Semilinear PDEs in Sobolev Spaces and Their Probabilistic Interpretation via the FBSDEs
• Weak solutions for SPDE's and backward doubly stochastic differential equations