Free Access
Issue
ESAIM: COCV
Volume 21, Number 4, October-December 2015
Page(s) 1150 - 1177
DOI https://doi.org/10.1051/cocv/2014062
Published online 06 July 2015
  1. G. Barles, Fully nonlinear Neumann type boundary conditions for second-order elliptic and parabolic equations. J. Differ. Equ. 106 (1993) 90–106. [CrossRef] [Google Scholar]
  2. J. Bismut, Conjugate convex functions in optimal stochastic control. J. Math. Anal. Appl. 44 (1973) 384–404. [CrossRef] [MathSciNet] [Google Scholar]
  3. J. Bismut, Contrôl des systèmes linéares quadratiques, in Applications de L’intégrale Stochastique, Séminaire de Probabilité XII, Vol. 649 of Lect. Notes Math. Springer, Berlin, Heidelberg, New York (1978) 180–264. [Google Scholar]
  4. J. Bismut, An introductory approach to duality in optimal stochastic control. SIAM Rev. 20 (1978) 62–78. [CrossRef] [MathSciNet] [Google Scholar]
  5. B. Boufoussi and J. Van Casteren, An approximation result for a nonlinear Neumann boundary value problem via BSDEs. Stoch. Proc. Appl. 114 (2004) 331–350. [CrossRef] [Google Scholar]
  6. M. Bourgoing, Viscosity solutions of fully nonlinear second order parabolic equations with L1-time dependence and Neumann boundary conditions. Available on http://www.phys.univ-tours.fr/˜barles/artL1-1.pdf. [Google Scholar]
  7. R. Buckdahn and J. Li, Stochastic differential games and viscosity solutions of Hamilton–Jacobi–Bellman–Isaacs equations. SIAM J. Control. Optim. 47 (2008) 444–475. [Google Scholar]
  8. M.G. Crandall, H. Ishii and P.L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1–67. [Google Scholar]
  9. R.W.R. Darling and E. Pardoux, Backwards SDE with random terminal time, and applications to semilinear elliptic PDE. Ann. Probab. 25 (1997) 1135–1159. [CrossRef] [MathSciNet] [Google Scholar]
  10. M.V. Day, Neumann-Type Boundary Conditions for Hamilton–Jacobi Equations in Smooth Domains. Appl. Math. Optim. 53 (2006) 359–381. [CrossRef] [MathSciNet] [Google Scholar]
  11. F. Delbaen and S. Tang, Harmonic analysis of stochastic equations and backward stochastic differential equations. Probab. Theory Relat. Fields 146 (2010) 291–336. [CrossRef] [Google Scholar]
  12. N. El Karoui, S. Peng and M.C. Quenez, Backward stochastic differential equations in finance. Math. Finance 7 (1997) 1–71. [CrossRef] [MathSciNet] [Google Scholar]
  13. Y. Hu, Probabilistic interpretation for a system of quasilinear elliptic partial differential equations with Neumann boundary conditions. Stochastic. Process. Appl. 48 (1993) 107–121. [Google Scholar]
  14. P.L. Lions, Neumann type boundary conditions for Hamilton–Jacobi equations. Duke Math. J. 52 (1985) 793–820. [CrossRef] [MathSciNet] [Google Scholar]
  15. P.L. Lions and A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 (1984) 511–537. [Google Scholar]
  16. J.L. Menaldi, Stochastic variational inequality for reflected diffusion. Indiana Univ. Math. J. 32 (1983) 733–744. [CrossRef] [MathSciNet] [Google Scholar]
  17. E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 (1990) 55–61. [Google Scholar]
  18. E. Pardoux and S. Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equations. Stochastic partial differential equations and their applications. Vol. 176 of Proc. IFIP Int. Conf., Charlotte/NC (USA) (1991), Lect. Notes Control Inf. Sci. Springer (1992) 200–217. [Google Scholar]
  19. E. Pardoux and R.J. Williams, Symmetric reflected diffusions. Ann. Inst. Henri Poincaré 30 (1994) 13–62. [Google Scholar]
  20. E. Pardoux and S. Zhang, Generalized BSDEs and nonlinear Neumann boundary value problems. Probab. Theory Relat. Fields 110 (1998) 535–558. [Google Scholar]
  21. S. Peng, BSDE and stochastic optimizations (in Chinese), in: Chap. 2 of Topics in stochastic analysis, edited by J. Yan, S. Peng, S. Fang and L. Wu. Science Press, Beijing (1997). [Google Scholar]
  22. S. Peng, A generalized dynamic programming principle and Hamilton–Jacobi–Bellman equation. Stoch. Stoch. Rep. 38 (1992) 119–134. [CrossRef] [Google Scholar]
  23. Y. Saisho, Stochastic differential equations for multidimensional domains with refecting boundary. Probab. Theory Relat. Fields 74 (1987) 455-477. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.