Geodesic
On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients
Algebra i analiz, Tome 17 (2005) no. 2, pp. 108-132.

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Elliptic Bellman equations with coefficients independent of the variable $x$ are considered. Error bounds for certain types of finite-difference schemes are obtained. These estimates are sharper than the earlier results in [8]. 
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Hongjie Dong; N. V. Krylov. On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients. Algebra i analiz, Tome 17 (2005) no. 2, pp. 108-132. http://geodesic.mathdoc.fr/item/AA_2005_17_2_a4/

[1] Barles G., Jakobsen E. R., “On the convergence rate of approximation schemes for Hamilton–Jacobi–Bellman equations”, M2AN Math. Model. Numer. Anal., 36:1 (2002), 33–54 | DOI | MR | Zbl

[2] Barles G., Jakobsen E. R., “Error bounds for monotone approximation schemes for Hamilton–Jacobi–Bellman equations”, SIAM J. Numer. Anal., 43:2 (2005), 540–558 | DOI | MR | Zbl

[3] Fleming W. H., Soner H. M., Controlled Markov processeseand viscosity solutions, Appl. Math. (New York), 25, Springer-Verlag, New York, 1993 | MR | Zbl

[4] Friedman A., Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1964 | MR | Zbl

[5] Krylov H. V., Upravlyaemye protsessy diffuzionnogo tipa, Nauka, M., 1977 | MR

[6] Krylov N. V., Nelineinye ellipticheskie i parabolicheskie uravneniya vtorogo poryadka, Nauka, M., 1985 | MR

[7] Krylov N. V., “On the general notion of fully nonlinear second-order elliptic equation”, Trans. Amer. Math. Soc., 347:3 (1995), 857–895 | DOI | MR | Zbl

[8] Krylov N. V., “On the rate of convergence of finite-difference approximations for Bellman's equations”, Algebra i analiz, 9:3 (1997), 245–256 | MR | Zbl

[9] Krylov N. V., “Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies”, Electron. J. Probab., 4, Paper No 2 (1999), 19 ; http://www.math.washington.edu/~ejpecp/EjpVol4/paper2.abs.html | MR | Zbl

[10] Krylov N. V., “Mean value theorems for stochastic integrals”, Ann. Probab., 29:1 (2001), 385–410 | DOI | MR | Zbl

[11] Safonov M. V., “O klassicheskom reshenii ellipticheskogo uravneniya Bellmana”, Dokl. AN SSSR, 278:4 (1984), 810–813 | MR | Zbl