ERROR ESTIMATES FOR SECOND ORDER HAMILTON-JACOBI-BELLMAN EQUATIONS. APPROXIMATION OF PROBABILISTIC REACHABLE SETS

摘要

This work deals with numerical approximations of unbounded and discontinuous value functions associated to some stochastic control problems. We derive error estimates for monotone schemes based on a Semi-Lagrangian method (or more generally in the form of a Markov chain approximation). A motivation of this study consists in approximating chance-constrained reachability sets. The latters will be characterized as level sets of a discontinuous value function associated to an adequate stochastic control problem. A precise analysis of the level-set approach is carried out and some numerical simulations are given to illustrate the approach.