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Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations. (English) Zbl 1123.65096

This paper is concerned with error estimations of numerical approximations for viscosity solutions associated with parabolic Hamilton-Jacobi-Bellman equations. The authors provide nonsymmetric upper and lower bounds for the rate of convergence. These results are applied to various schemes including Crank-Nicolson type finite difference schemes, splitting methods and classical approximation by piecewise constant controls.

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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