[1] Briand P, Delyon B, Hu Y, Pardoux E, Stoica L. Lp solutions of backward stochastic differential equations. Stoch Process Appl, 2003, 108(4):604-618 [2] Buckdahn R, Keller C, Ma J, Zhang J. Pathwise viscosity solutions of stochastic PDEs and forward pathdependent PDEs-a rough path view. arXiv:1501.06978, 2015 [3] Buckdahn R, Ma J. Pathwise stochastic control problems and stochastic HJB equations. SIAM J Control Optim, 2007, 45(6):2224-2256 [4] Cont R, Fournié D -A, et al. Functional itô calculus and stochastic integral representation of martingales. The Annals of Probability, 2013, 41(1):109-133 [5] Crandall M G, Ishii H, Lions P -L. Users guide to viscosity solutions of second order partial differential equations. Bull Amer Math Soc, 1992, 27(1):1-67 [6] Crandall M G, Kocan M, Swiech A. Lp-theory for fully nonlinear uniformly parabolic equations. Commun Partial Differ Equ, 2000, 25(11/12):1997-2053 [7] Da Prato G, Zabczyk J. Stochastic equations in infinite dimensions. Cambridge University Press, 2014 [8] Du K, Qiu J, Tang S. Lp theory for super-parabolic backward stochastic partial differential equations in the whole space. Appl Math Optim, 2011, 65(2):175-219 [9] Ekren I, Keller C, Touzi N, Zhang J. On viscosity solutions of path dependent PDEs. Ann Probab, 2014, 42(1):204-236 [10] Ekren I, Touzi N, Zhang J. Viscosity solutions of fully nonlinear parabolic path dependent PDEs:Part I. Ann Probab, 2016, 44(2):1212-1253 [11] Gawarecki L, Mandrekar V. Stochastic differential equations in infinite dimensions:with applications to stochastic partial differential equations. Springer Science & Business Media, 2010 [12] Horst U, Qiu J, Zhang Q. A constrained control problem with degenerate coefficients and degenerate backward SPDEs with singular terminal condition. SIAM J Control Optim, 2016, 54(2):946-963 [13] Hu Y, Ma J, Yong J. On semi-linear degenerate backward stochastic partial differential equations. Probab Theory Relat Fields, 2002, 123:381-411 [14] Juutinen P. On the definition of viscosity solutions for parabolic equations. Proceedings of the American Mathematical Society, 2001, 129(10):2907-2911 [15] Krylov N V. Boundedly nonhomogeneous elliptic and parabolic equations. Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1982, 46(3):487-523 [16] Krylov N V. Nonlinear Elliptic and Parabolic Equations of the Second Order. Dordrecht:D Reidel, 1987 [17] Leão D, Ohashi A, Simas A. A weak version of path-dependent functional Itô calculus. Ann Probab, 2018, 46(6):3399-3441 [18] Lions P, Souganidis P. Fully nonlinear stochastic partial differential equations:Non-smooth equations and applications. C R Acad Sci paris, 1998, 327(1):735-741 [19] Lions P L. Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Part Ⅱ. Commun Partial Differ Equ, 1983, 8:1229-1276 [20] Lukoyanov N Y. On viscosity solution of functional hamilton-jacobi type equations for hereditary systems. Proceedings of the Steklov Institute of Mathematics, 2007, 259(2):S190-S200 [21] Ma J, Yin H, Zhang J. On non-Markovian forward-backward SDEs and backward stochastic PDEs. Stoch Process Appl, 2012, 122(12):3980-4004 [22] Øksendal B. Stochastic differential equations. Springer, 2003 [23] Pardoux E. Stochastic partial differential equations and filtering of diffusion processes. Stoch, 1979:127-167 [24] Peng S. Stochastic Hamilton-Jacobi-Bellman equations. SIAM J Control Optim, 1992, 30:284-304 [25] Peng S. Backward stochastic differential equation, nonlinear expectation and their applications. Proceedings of the International Congress of Mathematicians, 2010:393-432 [26] Peng S. Note on viscosity solution of path-dependent PDE and G-martingales. arXiv:1106.1144, 2011 [27] Qiu J. Weak solution for a class of fully nonlinear stochastic hamilton-jacobi-bellman equations. Stoch Process Appl, 2017, 127(6):1926-1959 [28] Qiu J. Viscosity solutions of stochastic Hamilton-Jacobi-Bellman equations. SIAM J Control Optim, 2018, 56(5):3708-3730 [29] Qiu J, Tang S. Maximum principles for backward stochastic partial differential equations. J Funct Anal, 2012, 262:2436-2480 [30] Tang S. Semi-linear systems of backward stochastic partial differential equations in Rn. Chin Ann Math, 2005, 26B(3):437-456 [31] Tang S, Wei W. On the cauchy problem for backward stochastic partial differential equations in Hölder spaces. Ann Probab, 2016, 44(1):360-398 [32] Wang L. On the regularity theory of fully nonlinear parabolic equations:I. Commun Pure Appl Math, 1992, 45(1):27-76 |