\(G\)-expectation weighted Sobolev spaces, backward SDE and path dependent PDE

DOI10.2969/jmsj/06741725zbMath1335.60098arXiv1305.4722OpenAlexW1569706336MaRDI QIDQ904206

Shige Peng, Yongsheng Song

Publication date: 12 January 2016

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.4722

zbMATH Keywords

backward stochastic differential equations\(G\)-Brownian motion\(G\)-martingale\(G\)-expectation weighted Soboloev spaces\(P\)-weighted Sobolev spacespath dependent partial differential equations

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Applications of stochastic analysis (to PDEs, etc.) (60H30) Second-order elliptic equations (35J15) Second-order parabolic equations (35K10)

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Quadratic backward stochastic differential equations driven by \(G\)-Brownian motion: discrete solutions and approximation, A weak version of path-dependent functional Itô calculus, Path dependent Feynman-Kac formula for forward backward stochastic Volterra integral equations, Sample path properties of \(G\)-Brownian motion, Zero-sum path-dependent stochastic differential games in weak formulation, Rough path analysis for local time of G-Brownian motion, Viscosity solutions to second order path-dependent Hamilton-Jacobi-Bellman equations and applications, Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs, Approximate viscosity solutions of path-dependent PDEs and Dupire's vertical differentiability, Survey on path-dependent PDEs, Backward stochastic differential equations driven by \(G\)-Brownian motion, Weak differentiability of Wiener functionals and occupation times, Properties of \(G\)-martingales with finite variation and the application to \(G\)-Sobolev spaces, Comparison of Viscosity Solutions of Semilinear Path-Dependent PDEs, Pseudo-Markovian viscosity solutions of fully nonlinear degenerate PPDEs, A martingale approach for fractional Brownian motions and related path dependent PDEs, Crandall-Lions viscosity solutions for path-dependent PDEs: the case of heat equation, Jensen's inequality for backward SDEs driven by \(G\)-Brownian motion

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