Multi-dimensional BSDEs driven by G-Brownian motion and related system of fully nonlinear PDEs

References

• G. Barles, R. Buckdahn, and E. Pardoux, Backward stochastic differential equations and integral-partial differential equations, Stoch. Stoch. Rep. 60(1–2) (1997), pp. 57–83.
   Google Scholar
• R. Buckdahn and Y. Hu, Probabilistic interpretation of a coupled system of Hamilton-Jacobi-Bellman equations, J. Evol. Equ. 10(3) (2010), pp. 529–549.
   Web of Science ®Google Scholar
• R. Buckdahn and J. Li, Stochastic differential games and viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations, SIAM J. Control Optim. 47(1) (2008), pp. 444–475.
   Web of Science ®Google Scholar
• F. Coquet, Y. Hu, J. Memin, and S. Peng, Filtration consistent nonlinear expectations and related g-expectations, Probab. Theory Relat. Fields 123(1) (2002), pp. 1–27.
   Web of Science ®Google Scholar
• L. Denis, M. Hu, and S. Peng, Function spaces and capacity related to a sublinear expectation: Application to G-Brownian motion paths, Potential Anal. 34(2) (2011), pp. 139–161.
   Web of Science ®Google Scholar
• N. El Karoui, S. Peng, and M.C. Quenez, Backward stochastic differential equations in finance, Math. Finance 7(1) (1997), pp. 1–71.
   Web of Science ®Google Scholar
• M. Hu and S. Peng, On representation theorem of G-expectations and paths of G-Brownian motion, Acta Math. Appl. Sin. Engl. Ser. 25(3) (2009), pp. 539–546.
   Web of Science ®Google Scholar
• M. Hu and F. Wang, Ergodic BSDEs driven by G-Brownian motion and applications, Stoch. Dyn. 18(6) (2018), pp. 1–35.
   Web of Science ®Google Scholar
• M. Hu, S. Ji, S. Peng, and Y. Song, Backward stochastic differential equations driven by G-Brownian motion, Stoch. Process. Appl. 124(1) (2014), pp. 759–784.
   Web of Science ®Google Scholar
• M. Hu, S. Ji, S. Peng, and Y. Song, Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion, Stoch. Process. Appl. 124(2) (2014), pp. 1170–1195.
   Web of Science ®Google Scholar
• M. Hu, F. Wang, and G. Zheng, Quasi-continuous random variables and processes under the G-expectation framework, Stoch. Process. Appl. 126(8) (2016), pp. 2367–2387.
   Web of Science ®Google Scholar
• H. Li, S. Peng, and A.S. Hima, Reflected solutions of backward stochastic differential equations driven by G-Brownian motion, Sci. China Math. 61(1) (2018), pp. 1–26.
   Web of Science ®Google Scholar
• E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Syst. Control Lett. 14(1) (1990), pp. 55–61.
   Web of Science ®Google Scholar
• E. Pardoux and S. Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equationsin Stochastic Partial Differential Equations and their Applications, Lect. Notes Control Inf. Sci. 176, Springer, Berlin, 1992, pp. 200–217.
   Google Scholar
• E. Pardoux, F. Pradeilles, and Z. Rao, Probabilistic interpretation of a system of semi-linear parabolic partial differential equations, Ann. Inst. H. Poincaré Probab. Statist. 33(4) (1997), pp. 467–490.
   Web of Science ®Google Scholar
• S. Peng, Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stoch. Stoch. Rep. 37(1–2) (1991), pp. 61–74.
   Google Scholar
• S. Peng, Backward stochastic differential equations and applications to optimal control, Appl. Math. Optim. 27(2) (1993), pp. 125–144.
   Web of Science ®Google Scholar
• S. Peng, G-expectation, G-Brownian motion and related stochastic calculus of Itô type in Stochastic Analysis and Applications, Abel Symp. 2, Springer, Berlin, 2007, pp. 541–567.
   Google Scholar
• S. Peng, Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation, Stoch. Process. Appl. 118(12) (2008), pp. 2223–2253.
   Web of Science ®Google Scholar
• S. Peng, Nonlinear expectations and stochastic calculus under uncertainty, (2010). Available at arXiv:1002.4546v1.
   Google Scholar
• H.M. Soner, N. Touzi, and J. Zhang, Wellposedness of second order backward SDEs, Probab. Theory Relat. Fields 153(1–2) (2012), pp. 149–190.
   Web of Science ®Google Scholar
• Y. Song, Some properties on G-evaluation and its applications to G-martingale decomposition, Sci. China Math. 54(2) (2011), pp. 287–300.
   Web of Science ®Google Scholar
• Y. Song, Properties of G-martingales with finite variation and the application to G-Sobolev spaces, Stoch. Process. Appl. 129(6) (2019), pp. 2066–2085.
   Web of Science ®Google Scholar