The obstacle problem for quasilinear stochastic PDE's

DOI10.1214/09-AOP507zbMath1200.60052arXiv1010.2307MaRDI QIDQ984447

Anis Matoussi, Lucretiu Stoica

Publication date: 19 July 2010

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

Full work available at URL: https://arxiv.org/abs/1010.2307

zbMATH Keywords

obstacle problemstochastic partial differential equationregular measurebackward doubly stochastic differential equationregular potential

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Martingales and classical analysis (60G46)

Related Items (17)

Weak solution for a class of fully nonlinear stochastic Hamilton-Jacobi-Bellman equations ⋮ The existence and uniqueness result for quasilinear stochastic PDEs with obstacle under weaker integrability conditions ⋮ Backward doubly SDEs and semilinear stochastic PDEs in a convex domain ⋮ The obstacle problem for quasilinear stochastic integral-partial differential equations ⋮ Second-order BSDEs with general reflection and game options under uncertainty ⋮ The obstacle problem for stochastic porous media equations ⋮ Necessary condition for optimal control of doubly stochastic systems ⋮ Reflected BSDEs and the obstacle problem for semilinear PDEs in divergence form ⋮ The obstacle problem for quasilinear stochastic PDEs: analytical approach ⋮ Reflected solutions of generalized anticipated backward double stochastic differential equations ⋮ Quasilinear stochastic PDEs with two obstacles: probabilistic approach ⋮ Large deviation principles of obstacle problems for quasilinear stochastic PDEs ⋮ The obstacle problem for quasilinear stochastic PDEs with degenerate operator ⋮ Wong-Zakai approximations of backward doubly stochastic differential equations ⋮ The obstacle problem for quasilinear stochastic PDEs with Neumann boundary condition ⋮ The obstacle problem for semilinear parabolic partial integro-differential equations ⋮ The obstacle problem for quasilinear stochastic PDEs with non-homogeneous operator

Cites Work

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• A general analytical result for non-linear {SPDE}'s and applications
• A probabilistic interpretation of the divergence and BSDE's.
• Weak solutions for SPDE's and backward doubly stochastic differential equations
• Stochastic PDEs driven by nonlinear noise and backward doubly SDEs

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