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Volumn 76, Issue 260, 2007, Pages 1861-1893

Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations

Author keywords

Approximation schemes; Convergence rate; Error bound; Finite difference methods; Hamilton Jacobi Bellman equations; Splitting methods; Switching system; Viscosity solution

Indexed keywords


EID: 38849122631     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-07-02000-5     Document Type: Article
Times cited : (107)

References (28)
  • 1
    • 0036012033 scopus 로고    scopus 로고
    • On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations
    • MR1916291 2003h:65142
    • G. Barles and E. R. Jakobsen. On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations. M2AN Math. Model. Numer. Anal. 36(1):33-54, 2002. MR1916291 (2003h:65142)
    • (2002) M2AN Math. Model. Numer. Anal , vol.36 , Issue.1 , pp. 33-54
    • Barles, G.1    Jakobsen, E.R.2
  • 2
    • 25444517488 scopus 로고    scopus 로고
    • Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations
    • MR2177879
    • G. Barles and E. R. Jakobsen. Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations. SIAM J. Numer. Anal. 43(2):540-558, 2005. MR2177879
    • (2005) SIAM J. Numer. Anal , vol.43 , Issue.2 , pp. 540-558
    • Barles, G.1    Jakobsen, E.R.2
  • 3
    • 84974753170 scopus 로고
    • Convergence of approximation schemes for fully nonlinear second order equations
    • MR1115933 92d:35137
    • G. Barles and P. E. Souganidis. Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Anal. 4(3):271-283, 1991. MR1115933 (92d:35137)
    • (1991) Asymptotic Anal , vol.4 , Issue.3 , pp. 271-283
    • Barles, G.1    Souganidis, P.E.2
  • 4
    • 4444313180 scopus 로고    scopus 로고
    • A fast algorithm for the two dimensional HJB equation of stochastic control
    • MR2087732 2005e:93165
    • F. Bonnans, E. Ottenwaelter, and H. Zidani. A fast algorithm for the two dimensional HJB equation of stochastic control. M2AN Math. Model. Numer. Anal. 38(4):723-735, 2004. MR2087732 (2005e:93165)
    • (2004) M2AN Math. Model. Numer. Anal , vol.38 , Issue.4 , pp. 723-735
    • Bonnans, F.1    Ottenwaelter, E.2    Zidani, H.3
  • 5
    • 3142693266 scopus 로고    scopus 로고
    • Consistency of generalized finite difference schemes for the stochastic HJB equation
    • MR2005192 2004i:49061
    • F. Bonnans and H. Zidani. Consistency of generalized finite difference schemes for the stochastic HJB equation. SIAM J. Numer. Anal. 41(3):1008-1021, 2003. MR2005192 (2004i:49061)
    • (2003) SIAM J. Numer. Anal , vol.41 , Issue.3 , pp. 1008-1021
    • Bonnans, F.1    Zidani, H.2
  • 6
    • 0002560251 scopus 로고
    • An approximation scheme for the optimal control of diffusion processes
    • MR1326802 96a:49033
    • F. Camilli and M. Falcone. An approximation scheme for the optimal control of diffusion processes. RAIRO Model. Math. Anal. Numer. 29(1): 97-122, 1995. MR1326802 (96a:49033)
    • (1995) RAIRO Model. Math. Anal. Numer , vol.29 , Issue.1 , pp. 97-122
    • Camilli, F.1    Falcone, M.2
  • 7
    • 0021202882 scopus 로고
    • Optimal switching for ordinary differential equations
    • MR728678 85b:49043
    • I. Capuzzo-Dolcetta and L. C. Evans. Optimal switching for ordinary differential equations. SIAM J. Control Optim. 22(1):143-161, 1984. MR728678 (85b:49043)
    • (1984) SIAM J. Control Optim , vol.22 , Issue.1 , pp. 143-161
    • Capuzzo-Dolcetta, I.1    Evans, L.C.2
  • 8
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • MR1118699 92j:35050
    • 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. (N.S.), 27(1):1-67, 1992. MR1118699 (92j:35050)
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 9
    • 84966245867 scopus 로고
    • Two approximations of solutions of Hamilton-Jacobi equations
    • MR744921 86j:65121
    • M. G. Crandall and P.-L. Lions. Two approximations of solutions of Hamilton-Jacobi equations. Math. Comp. 43(167):1-19, 1984. MR744921 (86j:65121)
    • (1984) Math. Comp , vol.43 , Issue.167 , pp. 1-19
    • Crandall, M.G.1    Lions, P.-L.2
  • 10
    • 85009826745 scopus 로고    scopus 로고
    • On the rate of convergence of finte-difference approximations for Bellman equations with constant coefficients
    • MR2159586 2006f:49050
    • H. Dong and N. V. Krylov. On the rate of convergence of finte-difference approximations for Bellman equations with constant coefficients. St. Petersburg Math. J. 17(2): 295-313, 2006. MR2159586 (2006f:49050)
    • (2006) St. Petersburg Math. J , vol.17 , Issue.2 , pp. 295-313
    • Dong, H.1    Krylov, N.V.2
  • 13
    • 0009426683 scopus 로고
    • Optimal stochastic switching and the Dirichlet problem for the Bellman equation
    • MR536953 80f:93091
    • L. C. Evans and A. Friedman. Optimal stochastic switching and the Dirichlet problem for the Bellman equation. Trans. Amer. Math. Soc. 253:365-389, 1979. MR536953 (80f:93091)
    • (1979) Trans. Amer. Math. Soc , vol.253 , pp. 365-389
    • Evans, L.C.1    Friedman, A.2
  • 14
    • 84990575194 scopus 로고
    • On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs
    • MR973743 89m:35070
    • H. Ishii. On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs. Comm. Pure Appl. Math., 42(1):15-45, 1989. MR973743 (89m:35070)
    • (1989) Comm. Pure Appl. Math , vol.42 , Issue.1 , pp. 15-45
    • Ishii, H.1
  • 15
    • 0010851810 scopus 로고
    • Viscosity solutions for monotone systems of second-order elliptic PDEs
    • MR1116855 92h:35066
    • H. Ishii and S. Koike. Viscosity solutions for monotone systems of second-order elliptic PDEs. Comm. Partial Differential Equations 16(6-7):1095-1128, 1991. MR1116855 (92h:35066)
    • (1991) Comm. Partial Differential Equations , vol.16 , Issue.6-7 , pp. 1095-1128
    • Ishii, H.1    Koike, S.2
  • 16
    • 0038412191 scopus 로고
    • Viscosity solutions of a system of nonlinear second-order elliptic PDEs arising in switching games
    • MR1116886 92h:35067
    • H. Ishii and S. Koike. Viscosity solutions of a system of nonlinear second-order elliptic PDEs arising in switching games. Funkcial. Ekvac., 34:143-155, 1991. MR1116886 (92h:35067)
    • (1991) Funkcial. Ekvac , vol.34 , pp. 143-155
    • Ishii, H.1    Koike, S.2
  • 17
    • 0038069084 scopus 로고    scopus 로고
    • On the rate of convergence of approximation schemes for Bellman equations associated with optimal stopping time problems
    • MR1978929 2004g:49054
    • E. R. Jakobsen. On the rate of convergence of approximation schemes for Bellman equations associated with optimal stopping time problems. Math. Models Methods Appl. Sci. (M3AS) 13(5):613-644, 2003. MR1978929 (2004g:49054)
    • (2003) Math. Models Methods Appl. Sci. (M3AS) , vol.13 , Issue.5 , pp. 613-644
    • Jakobsen, E.R.1
  • 18
    • 0037055768 scopus 로고    scopus 로고
    • Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations
    • MR1919788 2003i:35135
    • E. R. Jakobsen and K. H. Karlsen. Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations. J. Differential Equations 183:497-525, 2002. MR1919788 (2003i:35135)
    • (2002) J. Differential Equations , vol.183 , pp. 497-525
    • Jakobsen, E.R.1    Karlsen, K.H.2
  • 19
    • 0009900309 scopus 로고    scopus 로고
    • On the rate of convergence of finite-difference approximations for Bellman's equations
    • MR1466804 98h:49033
    • N. V. Krylov. On the rate of convergence of finite-difference approximations for Bellman's equations. St. Petersburg Math. J., 9(3):639-650, 1997. MR1466804 (98h:49033)
    • (1997) St. Petersburg Math. J , vol.9 , Issue.3 , pp. 639-650
    • Krylov, N.V.1
  • 20
    • 0034384390 scopus 로고    scopus 로고
    • On the rate of convergence of finite-difference approximations for Bellman's equations with variable coefficients
    • MR1759507 2001j:65134
    • N. V. Krylov. On the rate of convergence of finite-difference approximations for Bellman's equations with variable coefficients. Probab. Theory Relat. Fields, 117:1-16, 2000. MR1759507 (2001j:65134)
    • (2000) Probab. Theory Relat. Fields , vol.117 , pp. 1-16
    • Krylov, N.V.1
  • 21
    • 0007384270 scopus 로고    scopus 로고
    • Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies
    • MR1668597 2000b:49056
    • N. V. Krylov. Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies. Electron. J. Probab. 4(2), 1999. MR1668597 (2000b:49056)
    • (1999) Electron. J. Probab , vol.4 , Issue.2
    • Krylov, N.V.1
  • 22
    • 29644447250 scopus 로고    scopus 로고
    • On the rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients
    • MR2174020 2006k:65219
    • N. V. Krylov. On the rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients. Appl. Math. Optim. 52(2): 365-399, 2005. MR2174020 (2006k:65219)
    • (2005) Appl. Math. Optim , vol.52 , Issue.2 , pp. 365-399
    • Krylov, N.V.1
  • 23
    • 38849188908 scopus 로고    scopus 로고
    • Personal communication
    • P.-L. Lions. Personal communication.
    • Lions, P.-L.1
  • 24
    • 0009924773 scopus 로고
    • Approximation numérique des équations de Hamilton-Jacobi-Bellman.
    • MR596541 82b:65055
    • P.-L. Lions and B. Mercier. Approximation numérique des équations de Hamilton-Jacobi-Bellman. RAIRO Anal. Numér. 14(4):369-393, 1980. MR596541 (82b:65055)
    • (1980) RAIRO Anal. Numér , vol.14 , Issue.4 , pp. 369-393
    • Lions, P.-L.1    Mercier, B.2
  • 25
    • 0000564951 scopus 로고
    • Total-variation-diminishing time discretizations
    • MR963855 90a:65196
    • C.-W. Shu. Total-variation-diminishing time discretizations, SIAM J. Sci. Statist. Comput. 9(6):1073-1084, 1988. MR963855 (90a:65196)
    • (1988) SIAM J. Sci. Statist. Comput , vol.9 , Issue.6 , pp. 1073-1084
    • Shu, C.-W.1
  • 26
    • 46549091075 scopus 로고
    • Approximation schemes for viscosity solutions of Hamilton-Jacobi equations
    • MR803085 86k:35028
    • P. E. Souganidis. Approximation schemes for viscosity solutions of Hamilton-Jacobi equations. J. Differential Equations 59(1):1-43, 1985. MR803085 (86k:35028)
    • (1985) J. Differential Equations , vol.59 , Issue.1 , pp. 1-43
    • Souganidis, P.E.1
  • 27
    • 33644995184 scopus 로고    scopus 로고
    • Splitting methods for Hamilton-Jacobi equations
    • MR2201439 2006j:65254
    • A. Tourin. Splitting methods for Hamilton-Jacobi equations. Numer. Methods Partial Differential Equations, 22(2): 381-396, 2006. MR2201439 (2006j:65254)
    • (2006) Numer. Methods Partial Differential Equations , vol.22 , Issue.2 , pp. 381-396
    • Tourin, A.1
  • 28
    • 26444597126 scopus 로고
    • Viscosity solutions for a system of elliptic inequalities with bilateral obstacles
    • MR927191 88m:35061
    • N. Yamada. Viscosity solutions for a system of elliptic inequalities with bilateral obstacles. Funkcial. Ekvac. 30(2-3):417-425, 1987. MR927191 (88m:35061)
    • (1987) Funkcial. Ekvac , vol.30 , Issue.2-3 , pp. 417-425
    • Yamada, N.1


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