Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov for finite difference schemes in the stationary case with constant coefficients and in the time-dependent case with variable coefficients by using control theory and probabilistic methods. In this paper we are able to handle variable coefficients by a purely analytical method. In our opinion this way is far simpler and, for the cases we can treat, it yields a better rate of convergence than Krylov obtains in the variable coefficients case.
Mots-clés : Hamilton-Jacobi-Bellman equation, viscosity solution, approximation schemes, finite difference methods, convergence rate
@article{M2AN_2002__36_1_33_0,
author = {Barles, Guy and Jakobsen, Espen Robstad},
title = {On the convergence rate of approximation schemes for {Hamilton-Jacobi-Bellman} equations},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {33--54},
publisher = {EDP-Sciences},
volume = {36},
number = {1},
year = {2002},
doi = {10.1051/m2an:2002002},
mrnumber = {1916291},
zbl = {0998.65067},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2002002/}
}
TY - JOUR AU - Barles, Guy AU - Jakobsen, Espen Robstad TI - On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2002 SP - 33 EP - 54 VL - 36 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2002002/ DO - 10.1051/m2an:2002002 LA - en ID - M2AN_2002__36_1_33_0 ER -
%0 Journal Article %A Barles, Guy %A Jakobsen, Espen Robstad %T On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 33-54 %V 36 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2002002/ %R 10.1051/m2an:2002002 %G en %F M2AN_2002__36_1_33_0
Barles, Guy; Jakobsen, Espen Robstad. On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 1, pp. 33-54. doi : 10.1051/m2an:2002002. http://archive.numdam.org/articles/10.1051/m2an:2002002/
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