Open AccessError estimates for second order Hamilton-Jacobi-Bellman equations. Approximation of probabilistic reachable sets
Author(s) -
Mohamed Assellaou,
Olivier Bokanowski,
Hasnaa Zidani
Publication year - 2015
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2015.35.3933
Subject(s) - reachability , monotone polygon , markov chain , mathematics , probabilistic logic , approximations of π , set (abstract data type) , approximation error , hamilton–jacobi equation , stochastic control , mathematical optimization , optimal control , computer science , algorithm , statistics , geometry , programming language
International audienceThis 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