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Error estimates for second order Hamilton-Jacobi-Bellman equations. Approximation of probabilistic reachable sets

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  • 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.
    Mathematics Subject Classification: Primary: 65M15, 93E20; Secondary: 49L25.


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