Publications

2003

• Discrete approximation for a class of the Hamilton-Jacobi equation for an optimal control problem of a differential-algebraic system
  
  • Bonnans Frédéric
  • Chartier Philippe
  • Zidani Hasnaa
  Control and Cybernetics, Polish Academy of Sciences, 2003, 32 (1), pp.33-55.
• Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation
  
  • Bonnans Frédéric
  • Zidani Hasnaa
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2003, 41 (3), pp.1008-1021. 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 (10.1137/S0036142901387336)
  DOI : 10.1137/S0036142901387336
• Asympotical models for wave propagation in media includings slots
  
  • Tordeux Sébastien
  , 2003.