Free Access
Issue
ESAIM: M2AN
Volume 38, Number 4, July-August 2004
Page(s) 723 - 735
DOI https://doi.org/10.1051/m2an:2004034
Published online 15 August 2004
  1. G. Barles and E.R. Jakobsen, On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations. ESAIM: M2AN 36 (2002) 33–54. [CrossRef] [EDP Sciences]
  2. G. Barles and E.R. Jakobsen, Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations (to appear).
  3. G. Barles and P.E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Analysis 4 (1991) 271–283. [MathSciNet]
  4. J.F. Bonnans and H. Zidani, Consistency of generalized finite difference schemes for the stochastic HJB equation. SIAM J. Numer. Anal. 41 (2003) 1008–1021. [CrossRef] [MathSciNet]
  5. J.F. Bonnans, E. Ottenwaelter and H. Zidani, A fast algorithm for the two dimensional HJB equation of stochastic control. Technical report, INRIA (2004). Rapport de Recherche 5078.
  6. F. Camilli and M. Falcone, An approximation scheme for the optimal control of diffusion processes. RAIRO Modél. Math. Anal. Numér. 29 (1995) 97–122. [CrossRef] [EDP Sciences] [MathSciNet]
  7. W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions. Springer, New York (1993).
  8. R.L. Graham, D.E. Knuth and O. Patashnik, Concrete Mathematics, A Foundation For Computer Science. Addison-Wesley, Reading, MA (1994). Second edition.
  9. E.R. Jakobsen and K.H. Karlsen, Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations. J. Differ. Equations 183 (2002) 497–525. [CrossRef] [MathSciNet]
  10. N.V. Krylov, On the rate of convergence of finite-difference approximations for Bellman's equations with variable coefficients. Probab. Theory Related Fields 117 (2000) 1–16. [CrossRef] [MathSciNet]
  11. H.J. Kushner, Probability methods for approximations in stochastic control and for elliptic equations. Academic Press, New York (1977). Math. Sci. Engrg. 129.
  12. H.J. Kushner and P.G. Dupuis, Numerical methods for stochastic control problems in continuous time. Springer, New York, Appl. Math. 24 (2001). Second edition.
  13. P.-L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Part 2: Viscosity solutions and uniqueness. Comm. Partial Differential Equations 8 (1983) 1229–1276. [CrossRef] [MathSciNet]
  14. P.-L. Lions and B. Mercier, Approximation numérique des équations de Hamilton-Jacobi-Bellman. RAIRO Anal. Numér. 14 (1980) 369–393. [MathSciNet]
  15. J.-L. Menaldi, Some estimates for finite difference approximations. SIAM J. Control Optim. 27 (1989) 579–607. [CrossRef] [MathSciNet]

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