Quenched mass transport of particles towards a target
Bouchard, Bruno; Djehiche, Boualem; Kharroubi, Idris (2020), Quenched mass transport of particles towards a target, Journal of Optimization Theory and Applications. 10.1007/s10957-020-01704-y
TypeArticle accepté pour publication ou publié
Journal nameJournal of Optimization Theory and Applications
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Department of Mathematics [KTH Royal Institute of Technology]
Laboratoire de Probabilités, Statistiques et Modélisations [LPSM (UMR_8001)]
Abstract (EN)We consider the stochastic target problem of finding the collection of initial laws of a mean-field stochastic differential equation such that we can control its evolution to ensure that it reaches a prescribed set of terminal probability distributions, at a fixed time horizon. Here, laws are considered conditionally to the path of the Brownian motion that drives the system. We establish a version of the geometric dynamic programming principle for the associated reachability sets and prove that the corresponding value function is a viscosity solution of a geometric partial differential equation. This provides a characterization of the initial masses that can be almost-surely transported towards a given target, along the paths of a stochastic differential equation. Our results extend  to our setting.
Subjects / KeywordsMcKean-Vlasov SDEs; dynamic programming; stochastic target; mass transportion; viscosity solutions
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