hal-00989641
https://hal-ensta-paris.archives-ouvertes.fr/hal-00989641
doi:10.1137/S0036142901387336
[ENSTA] ENSTA Paris
[UMA_ENSTA] Unité de Mathématiques Appliquées (UMA)
Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation
Bonnans, Frédéric
Zidani, Hasnaa
ART
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
2003
en
SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics