A priori estimates of smoothness of solutions to difference Bellman equations with linear and quasilinear operators
Author:
N. V. Krylov
Journal:
Math. Comp. 76 (2007), 669698
MSC (2000):
Primary 65M15, 35J60, 93E20
Published electronically:
January 8, 2007
MathSciNet review:
2291833
Fulltext PDF Free Access
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Additional Information
Abstract: A priori estimates for finitedifference approximations for the first and secondorder derivatives are obtained for solutions of parabolic equations described in the title.
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Barles, G., and Jakobsen, E.R., Error bounds for monotone approximation schemes for parabolic HamiltonJacobiBellman equations, preprint.
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Dong, Hongjie and Krylov, N.V., On the rate of convergence of finitedifference approximations for parabolic Bellman equations with Lipschitz coefficients in cylindrical domains, submitted to Applied Math. and Optimization.
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Mathematics, vol. 14, SpringerVerlag, New YorkBerlin, 1980.
Translated from the Russian by A. B. Aries. MR 601776
(82a:60062)
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approximations for Bellman’s equations with variable
coefficients, Probab. Theory Related Fields 117
(2000), no. 1, 1–16. MR 1759507
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approximations for Bellman equations with Lipschitz coefficients,
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 1.
 Bonnans, J. F., Ottenwaelter, E., and Zidani, H., A fast algorithm for the two dimensional HJB equation of stochastic control, M2AN Math. Model. Numer. Anal., Vol. 38 (2004), No. 4, 723735. MR 2087732 (2005e:93165)
 2.
 Barles, G., and Jakobsen, E.R., On the convergence rate of approximation schemes for HamiltonJacobiBellman equations, Mathematical Modelling and Numerical Analysis, ESAIM, M2AM, Vol. 36 (2002), No. 1, 3354. MR 1916291 (2003h:65142)
 3.
 Barles, G., and Jakobsen, E.R., Error bounds for monotone approximation schemes for HamiltonJacobiBellman equations, SIAM J. Numer. Anal., Vol. 43 (2005), No. 2, 540558. MR 2177879
 4.
 Barles, G., and Jakobsen, E.R., Error bounds for monotone approximation schemes for parabolic HamiltonJacobiBellman equations, preprint.
 5.
 Dong, Hongjie and Krylov, N.V., On the rate of convergence of finitedifference approximations for Bellman equations with constant coefficients, Algebra i Analiz (St. Petersburg Math. J.), Vol. 17 (2005), No. 2, 108132. MR 2159586 (2006f:49050)
 6.
 Dong, Hongjie and Krylov, N.V., On the rate of convergence of finitedifference approximations for degenerate linear parabolic equations with and coefficients, Electron. J. Diff. Eqns., Vol. 2005 (2005), No. 102, pp. 125. http://ejde.math.txstate.edu MR 2162263 (2006i:35008)
 7.
 Dong, Hongjie and Krylov, N.V., On the rate of convergence of finitedifference approximations for parabolic Bellman equations with Lipschitz coefficients in cylindrical domains, submitted to Applied Math. and Optimization.
 8.
 Jakobsen, E. R., On the rate of convergence of approximation schemes for Bellman equations associated with optimal stopping time problems, Math. Models Methods Appl. Sci., Vol. 13 (2003), No. 5, 613644. MR 1978929 (2004g:49054)
 9.
 Krylov, N.V., ``Controlled diffusion processes'', Nauka, Moscow, 1977 in Russian; English translation Springer, 1980. MR 601776 (82a:60062)
 10.
 Krylov, N.V., On the rate of convergence of finitedifference approximations for Bellman's equations, Algebra i Analiz, St. Petersburg Math. J., Vol. 9 (1997), No. 3, 245256. MR 1466804 (98h:49033)
 11.
 Krylov, N.V., Approximating value functions for controlled degenerate diffusion processes by using piecewise constant policies, Electronic Journal of Probability, Vol. 4 (1999), paper no. 2, 119, http://www.math.washington.edu/~ejpecp/EjpVol4/ paper2.abs.html. MR 1668597 (2000b:49056)
 12.
 Krylov, N.V., On the rate of convergence of finitedifference approximations for Bellman's equations with variable coefficients, Probab. Theory Relat. Fields, Vol. 117 (2000), No. 1, 116. MR 1759507 (2001j:65134)
 13.
 Krylov, N.V., The rate of convergence of finitedifference approximations for Bellman equations with Lipschitz coefficients, Applied Math. and Optimization, Vol. 52 (2005), No. 3, 365399. MR 2174020 (2006k:65219)
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Additional Information
N. V. Krylov
Affiliation:
Department of Mathematics, University of Minnesota, 127 Vincent Hall, Minneapolis, Minnesota 55455
Email:
krylov@math.umn.edu
DOI:
http://dx.doi.org/10.1090/S0025571807019539
PII:
S 00255718(07)019539
Keywords:
Finitedifference approximations,
Bellman equations,
fully nonlinear equations.
Received by editor(s):
November 13, 2005
Received by editor(s) in revised form:
May 14, 2006
Published electronically:
January 8, 2007
Additional Notes:
The work was partially supported by NSF Grant DMS0140405
Article copyright:
© Copyright 2007
American Mathematical Society
