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Algebra i Analiz, 1997, Volume 9, Issue 3, Pages 245–256 (Mi aa802)  

This article is cited in 67 scientific papers (total in 67 papers)

On the rate of convergence of finite-difference approximations for Bellman's equations

N. V. Krylov

School of Mathematics, University of Minnesota, Minneapolis, MN
Abstract: Some estimates are presented for the elliptic and parabolic Bellman equations with “constant” coefficients; these estimates are sharper than those announced earlier by the author in [8].
Keywords: Finite-difference approximations, Bellman's equations, fully nonlinear equations.
Received: 26.12.1996
Bibliographic databases:
Language: English
Citation: N. V. Krylov, “On the rate of convergence of finite-difference approximations for Bellman's equations”, Algebra i Analiz, 9:3 (1997), 245–256; St. Petersburg Math. J., 9:3 (1998), 639–650
Citation in format AMSBIB
\Bibitem{Kry97}
\by N.~V.~Krylov
\paper On the rate of convergence of finite-difference
approximations for Bellman's equations
\jour Algebra i Analiz
\yr 1997
\vol 9
\issue 3
\pages 245--256
\mathnet{http://mi.mathnet.ru/aa802}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1466804}
\zmath{https://zbmath.org/?q=an:0902.65035}
\transl
\jour St. Petersburg Math. J.
\yr 1998
\vol 9
\issue 3
\pages 639--650
Linking options:
  • https://www.mathnet.ru/eng/aa802
  • https://www.mathnet.ru/eng/aa/v9/i3/p245
  • This publication is cited in the following 67 articles:
    1. Jiang L., “Discrete-Time Approximation For Stochastic Optimal Control Problems Under the G-Expectation Framework”, Optim. Control Appl. Methods, 43:2 (2022), 418–434  crossref  isi
    2. Ferretti R., Sassi A., Zidani H., “Error Estimates For Numerical Approximation of Hamilton-Jacobi Equations Related to Hybrid Control Systems”, Appl. Math. Optim., 83:1 (2021), 139–175  crossref  isi
    3. Briand Ph., Geiss Ch., Geiss S., Labart C., “Donsker-Type Theorem For Bsdes: Rate of Convergence”, Bernoulli, 27:2 (2021), 899–929  crossref  isi
    4. Bian B., Chen X., Dai M., Qian Sh., “Penalty Method For Portfolio Selection With Capital Gains Tax”, Math. Financ., 31:3 (2021), 1013–1055  crossref  isi
    5. Picarelli A. Reisinger Ch. Arto J.R., “Some Regularity and Convergence Results For Parabolic Hamilton-Jacobi-Bellman Equations in Bounded Domains”, J. Differ. Equ., 268:12 (2020), 7843–7876  crossref  isi
    6. Krylov N.V., “On Shige Peng'S Central Limit Theorem”, Stoch. Process. Their Appl., 130:3 (2020), 1426–1434  crossref  isi
    7. Picarelli A., Reisinger Ch., “Duality-Based a Posteriori Error Estimates For Some Approximation Schemes For Optimal Investment Problems”, Comput. Math. Appl., 79:7 (2020), 2099–2118  crossref  isi
    8. Picarelli A., Reisinger Ch., “Probabilistic Error Analysis For Some Approximation Schemes to Optimal Control Problems”, Syst. Control Lett., 137 (2020), UNSP 104619  crossref  isi
    9. Huang Sh., Liang G., Zariphopoulou T., “An Approximation Scheme For Semilinear Parabolic Pdes With Convex and Coercive Hamiltonians”, SIAM J. Control Optim., 58:1 (2020), 165–191  crossref  isi
    10. Arakelyan A., Barkhudaryan R., Shahgholian H., Salehi M., “Numerical Treatment to a Non-Local Parabolic Free Boundary Problem Arising in Financial Bubbles”, Bull. Iran Math. Soc., 45:1 (2019), 59–73  crossref  mathscinet  zmath  isi  scopus
    11. Chen H., Huang G., Wang X.-J., “Convergence Rate Estimates For Aleksandrov'S Solution to the Monge-Ampere Equation”, SIAM J. Numer. Anal., 57:1 (2019), 173–191  crossref  mathscinet  zmath  isi  scopus
    12. Salgado A.J., Zhang W., “Finite Element Approximation of the Isaacs Equation”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 53:2 (2019), 351–374  crossref  mathscinet  isi  scopus
    13. Biswas I.H., Chowdhury I., Jakobsen E.R., “On the Rate of Convergence For Monotone Numerical Schemes For Nonlocal Isaacs Equations”, SIAM J. Numer. Anal., 57:2 (2019), 799–827  crossref  isi
    14. Nochetto R.H., Zhang W., “Discrete Abp Estimate and Convergence Rates For Linear Elliptic Equations in Non-Divergence Form”, Found. Comput. Math., 18:3 (2018), 537–593  crossref  mathscinet  isi  scopus  scopus
    15. Bokanowski O., Picarelli A., Reisinger Ch., “High-Order Filtered Schemes For Time-Dependent Second Order Hjb Equations”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 52:1 (2018), 69–97  crossref  isi
    16. Li Ya. Zhang Zh. Hu B., “Convergence Rate of An Explicit Finite Difference Scheme For a Credit Rating Migration Problem”, SIAM J. Numer. Anal., 56:4 (2018), 2430–2460  crossref  mathscinet  zmath  isi  scopus
    17. Neilan M., Salgado A.J., Zhang W., “Numerical Analysis of Strongly Nonlinear PDEs”, Acta Numer., 26 (2017), 137–303  crossref  mathscinet  zmath  isi  scopus
    18. Reisinger C., Forsyth P.A., “Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations”, Appl. Numer. Math., 103 (2016), 27–47  crossref  mathscinet  zmath  isi  scopus
    19. Bokanowski O., Picarelli A., Zidani H., “Dynamic Programming and Error Estimates For Stochastic Control Problems With Maximum Cost”, Appl. Math. Optim., 71:1 (2015), 125–163  crossref  mathscinet  zmath  isi  scopus  scopus
    20. Turanova O., “Error Estimates For Approximations of Nonhomogeneous Nonlinear Uniformly Elliptic Equations”, Calc. Var. Partial Differ. Equ., 54:3 (2015), 2939–2983  crossref  mathscinet  zmath  isi  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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