Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation

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
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Submitted on : Monday, May 12, 2014 - 11:09:40 AM
Last modification on : Wednesday, July 3, 2019 - 10:48:04 AM

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Frédéric Bonnans, Hasnaa Zidani. Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2003, 41 (3), pp.1008-1021. ⟨10.1137/S0036142901387336⟩. ⟨hal-00989641⟩

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