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Pré-Publication, Document De Travail Année : 2017

Quenched mass transport of particles towards a target

Résumé

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 [16] to our setting.
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Dates et versions

hal-01567312 , version 1 (22-07-2017)
hal-01567312 , version 2 (31-10-2018)
hal-01567312 , version 3 (19-11-2020)

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Bruno Bouchard, Boualem Djehiche, Idris Kharroubi. Quenched mass transport of particles towards a target. 2017. ⟨hal-01567312v1⟩
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