Error estimates for stochastic differential games: the adverse stopping case

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. To obtain the upper error bound, we consider the ‘Krylov regularization’ of the Isaacs equation to build an ap...

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Bibliographic Details
Published in:IMA journal of numerical analysis 2006-01, Vol.26 (1), p.188-212
Main Authors: Bonnans, J. Frédéric, Maroso, Stefania, Zidani, Housnaa
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
error estimates
Exact sciences and technology
finite differences
Hamilton–Jacobi–Bellman equation
Isaacs equation
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Partial differential equations
Sciences and techniques of general use
stochastic differential games
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Summary: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. To obtain the upper error bound, we consider the ‘Krylov regularization’ of the Isaacs equation to build an approximate sub-solution of the scheme. To get the lower error bound, we extend the method of Barles & Jakobsen (2005, SIAM J. Numer. Anal.) which consists in introducing a switching system whose solutions are local super-solutions of the Isaacs equation.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/dri034