Error estimates for stochastic differential games: the adverse stopping case |
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| Authors: | Bonnans, J. Frederic Maroso, Stefania Zidani, Housnaa |
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| Affiliation: | 1 Projet Sydoco, Inria-Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay, France, 2 Projet Sydoco, Inria-Rocquencourt and Unité de Mathématiques Appliquées, ENSTA, 32 Boulevard Victor, 75739 Paris Cedex 15, France |
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| Abstract: | ** Email: frederic.bonnans{at}inria.fr*** Email: stefania.maroso{at}inria.fr**** Email: zidani{at}ensta.fr We obtain error bounds for monotone approximation schemes ofa particular Isaacs equation. This is an extension of the theoryfor estimating errors for the HamiltonJacobiBellmanequation. To obtain the upper error bound, we consider the Krylovregularization of the Isaacs equation to build an approximatesub-solution of the scheme. To get the lower error bound, weextend the method of Barles & Jakobsen (2005, SIAM J. Numer.Anal.) which consists in introducing a switching system whosesolutions are local super-solutions of the Isaacs equation. |
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| Keywords: | Isaacs equation Hamilton– Jacobi– Bellman equation stochastic differential games finite differences error estimates |
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