Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation

Frédéric Bonnans and Hasnaa Zidani

2003

Publication type:

Paper in peer-reviewed journals

Journal:

SIAM Journal on Numerical Analysis, vol. 41(3), pp. 1008-1021

DOI:

10.1137/S0036142901387336

HAL:

hal-00989641

Abstract:

We analyze a class of numerical schemes for solving the HJB equation for stochastic control problems, which enters the framework of Markov chain approximations and generalizes the usual finite difference method. The latter is known to be monotonic, and hence valid, only if the scaled covariance matrix is dominant diagonal. We generalize this result by, given the set of neighboring points allowed to enter the scheme, showing how to compute effectively the class of covariance matrices that is consistent with this set of points. We perform this computation for several cases in dimensions 2, 3, and 4. Copyright © 2003 Society for Industrial and Applied Mathematics

BibTeX:

@article{Bon-Zid-2003,
    author={Frédéric Bonnans and Hasnaa Zidani },
    title={Consistency of Generalized Finite Difference Schemes for the 
           Stochastic HJB Equation },
    doi={10.1137/S0036142901387336 },
    journal={SIAM Journal on Numerical Analysis },
    year={2003 },
    volume={41(3) },
    pages={1008--1021},
}