Under smoothness conditions on the coefficients, the solution map of a mean-field G-SDE is Fréchet differentiable up to second order, with derivatives characterized as solutions of new G-SDEs.
BSDEs driven by G-Brownian motion under degenerate case and its application to the regularity of fully nonlinear PDEs
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abstract
In this paper, we obtain the existence and uniqueness theorem for backward stochastic differential equation driven by G-Brownian motion (G-BSDE) under degenerate case. Moreover, we propose a new probabilistic method based on the representation theorem of G-expectation and weak convergence to obtain the regularity of fully nonlinear PDE associated to G-BSDE.
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Regularity of Solutions of Mean-Field $G$-SDEs
Under smoothness conditions on the coefficients, the solution map of a mean-field G-SDE is Fréchet differentiable up to second order, with derivatives characterized as solutions of new G-SDEs.