Error estimates for a stochastic impulse control problem
Résumé
We obtain error bounds for monotone approximation schemes of a stochastic impulse control problem. This is an extension of the theory for error estimates for the Hamilton-Jacobi-Bellman equation. For obtaining these bounds we build a sequence of stochastic impulse control problems, and a sequence of monotone approximation schemes. Extending methods of Barles and Jakobsen , we give error estimate for each problem of the sequence. Using these bounds we obtain the result. We obtain the same estimate on the rate of convergence as in the equation without impulsions .