Journal Articles Discrete and Continuous Dynamical Systems - Series A Year : 2015

Error Estimates for Second Order Hamilton-Jacobi-Bellman Equations. Approximation of Probabilistic Reachable Sets

Mohamed Assellaou
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Olivier Bokanowski
Hasnaa Zidani

Abstract

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 discontinuous value functions associated to adequate stochastic control problems. A precise analysis of the level-set approach is carried out and some numerical simulations are given to illustrate the approach.
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Dates and versions

hal-00998371 , version 1 (02-06-2014)
hal-00998371 , version 2 (27-07-2015)

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Mohamed Assellaou, Olivier Bokanowski, Hasnaa Zidani. Error Estimates for Second Order Hamilton-Jacobi-Bellman Equations. Approximation of Probabilistic Reachable Sets. Discrete and Continuous Dynamical Systems - Series A, 2015, 35 (9), pp.3933 - 3964. ⟨10.3934/dcds.2015.35.3933⟩. ⟨hal-00998371v2⟩
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