Weak Solutions of Semilinear PDEs in Sobolev Spaces and Their Probabilistic Interpretation via the FBSDEs

DOI10.1080/07362990600753601zbMath1128.35109OpenAlexW1966552233MaRDI QIDQ5484533

Isabelle Turpin, Youssef Ouknine

Publication date: 21 August 2006

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

Full work available at URL: https://doi.org/10.1080/07362990600753601

zbMATH Keywords

weighted Sobolev spacebackward stochastic differential equationsemilinear parabolic PDESobolev solutionforward stochastic differential equation

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)

Related Items (7)

Classical and weak solutions of the partial differential equations associated with a class of two-point boundary value problems ⋮ Existence and Uniqueness of Multidimensional BSDEs and of Systems of Degenerate PDEs with Superlinear Growth Generator ⋮ WEAK SOLUTIONS OF SEMILINEAR PDEs WITH OBSTACLE(S) IN SOBOLEV SPACES AND THEIR PROBABILISTIC INTERPRETATION VIA THE RFBSDEs AND DRFBSDEs ⋮ Probabilistic interpretation for Sobolev solutions of McKean-Vlasov partial differential equations ⋮ Interior gradient and Hessian estimates for the Dirichlet problem of semi-linear degenerate elliptic systems: a probabilistic approach ⋮ Sobolev weak solutions for parabolic PDEs and FBSDEs ⋮ The obstacle problem for semilinear parabolic partial integro-differential equations

Cites Work

• Formes de Dirichlet générales et densité des variables aléatoires réelles sur l'espace de Wiener. (General Dirichlet forms and density of real random variables on Wiener space)
• Dirichlet forms and analysis on Wiener space
• Stochastic flows acting on Schwartz distributions
• Generalized directional gradients, backward stochastic differential equations and mild solutions of semilinear parabolic equations
• Weak solutions for SPDE's and backward doubly stochastic differential equations

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