Error estimates for stochastic differential games: the adverse stopping case

J. Frederic Bonnans (1) , Stefania Maroso (1) , Hasnaa Zidani (1)

1 SYDOCO - Dynamic systems, optimisation and optimal command

We obtain error bounds for monotone approximation schemes of a particular Isaacs equation. This is an extension of the theory for estimating errors for the Hamilton-Jacobi-Bellman equation. For obtaining upper error bound, we consider the ``Krylov regularization'' of the Isaacs equation to build an approximate sub-solution of the scheme. To get lower error bound we extend the method of Barles and Jakobsen which consists in introducing a switching system whose solutions are local super-solutions of the Isaacs equation.

Mots clés: ISAACS EQUATION; HAMILTON-JACOBI-BELLMAN EQUATION; STOCHASTIC DIFFERENTIAL GAMES; FINITE DIFFERENCES; ERROR ESTIMATES

Domaines: Autre [cs.OH]; Optimisation et contrôle [math.OC]

J. Frederic Bonnans, Stefania Maroso, Hasnaa Zidani. Error estimates for stochastic differential games: the adverse stopping case. [Research Report] RR-5441, INRIA. 2004, pp.28. ⟨inria-00070566⟩