Survey on path-dependent PDEs

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Nonlinear first-order PDEs (35F20) Second-order parabolic equations (35K10)

Cites Work

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Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations
Viscosity solutions of fully nonlinear parabolic path dependent PDEs. I.
Viscosity solutions of fully nonlinear parabolic path dependent PDEs. II
Viscosity solutions of fully nonlinear elliptic path dependent partial differential equations
Adapted solution of a backward stochastic differential equation
On viscosity solution of functional Hamilton-Jacobi type equations for hereditary systems
Decoupled mild solutions of path-dependent PDEs and integro PDEs represented by BSDEs driven by cadlag martingales
A functional extension of the Ito formula
\(G\)-expectation weighted Sobolev spaces, backward SDE and path dependent PDE
Change of variable formulas for non-anticipative functionals on path space
A weak version of path-dependent functional Itô calculus
Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III: Uniqueness of viscosity solutions for general second-order equations
Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. I: The case of bounded stochastic evolutions
Functional Itō calculus and stochastic integral representation of martingales
Properties of \(G\)-martingales with finite variation and the application to \(G\)-Sobolev spaces
Strong-viscosity solutions: classical and path-dependent PDEs
Crandall-Lions viscosity solutions for path-dependent PDEs: the case of heat equation
A martingale approach for fractional Brownian motions and related path dependent PDEs
Backward stochastic differential equations driven by \(G\)-Brownian motion
On viscosity solutions of path dependent PDEs
Nonlinear expectations and nonlinear Markov chains
BSDEs with jumps and path-dependent parabolic integro-differential equations
Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation
BSDE, path-dependent PDE and nonlinear Feynman-Kac formula
Viscosity Solutions of Hamilton-Jacobi Equations
Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
User’s guide to viscosity solutions of second order partial differential equations
Perron’s method for viscosity solutions of semilinear path dependent PDEs
Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs
Path-dependent BSDEs with jumps and their connection to PPIDEs
Nonlinear Expectations and Stochastic Calculus under Uncertainty
Functional Itô calculus
Backward Stochastic Differential Equations
An Overview of Viscosity Solutions of Path-Dependent PDEs

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