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• W1569706336 abstract "We introduce a new notion of G-expectation-weighted Sobolev spaces, or in short, G-Sobolev spaces, and prove that a backward SDEs driven by G-Brownian motion are in fact path dependent PDEs in the corresponding Sobolev spaces under G-norms. For the linear case of G corresponding the classical Wiener probability space with Wiener measure P, we have established a 1-1 correspondence between BSDE and such new type of quasilinear PDE in the corresponding P-Sobolev space. When G is nonlinear, we also provide such 1-1 correspondence between a fully nonlinear PDE in the corresponding G-Sobolev space and BSDE driven by G-Brownian. Consequently, the existence and uniqueness of such type of fully nonlinear path-dependence PDE in G-Sobolev space have been obtained via a recent results of BSDE driven by G-Brownian motion." @default.
• W1569706336 created "2016-06-24" @default.
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• W1569706336 date "2015-10-01" @default.
• W1569706336 modified "2023-09-26" @default.
• W1569706336 title "$G$-expectation weighted Sobolev spaces, backward SDE and path dependent PDE" @default.
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• W1569706336 doi "https://doi.org/10.2969/jmsj/06741725" @default.
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