BSDEs driven by \(G\)-Brownian motion under degenerate case and its application to the regularity of fully nonlinear PDEs

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Nonlinear processes (e.g., (G)-Brownian motion, (G)-Lévy processes) (60G65)

Cites Work

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Quasi-continuous random variables and processes under the \(G\)-expectation framework
Dynamic programming principle for stochastic recursive optimal control problem driven by a \(G\)-Brownian motion
Wellposedness of second order backward SDEs
Some properties on \(G\)-evaluation and its applications to \(G\)-martingale decomposition
Martingale representation theorem for the \(G\)-expectation
Function spaces and capacity related to a sublinear expectation: application to \(G\)-Brownian motion paths
Filtration consistent nonlinear expectations and evaluations of contingent claims
Explicit solutions of the \(G\)-heat equation for a class of initial conditions
A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
On representation theorem of \(G\)-expectations and paths of \(G\)-Brownian motion
Quadratic backward stochastic differential equations driven by \(G\)-Brownian motion: discrete solutions and approximation
Reflected solutions of backward stochastic differential equations driven by \(G\)-Brownian motion
Second order backward SDE with random terminal time
Backward stochastic differential equations driven by \(G\)-Brownian motion
Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by \(G\)-Brownian motion
Nonlinear expectations and nonlinear Markov chains
Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation
Stochastic maximum principle for stochastic recursive optimal control problem under volatility ambiguity
Optimal investment under model uncertainty in nondominated models
Two Person Zero-Sum Game in Weak Formulation and Path Dependent Bellman--Isaacs Equation
User’s guide to viscosity solutions of second order partial differential equations
Nonlinear Expectations and Stochastic Calculus under Uncertainty
ROBUST UTILITY MAXIMIZATION IN NONDOMINATED MODELS WITH 2BSDE: THE UNCERTAIN VOLATILITY MODEL

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