Quenched mass transport of particles towards a target
Abstract
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.
Keywords
Cite
@article{arxiv.1707.07869,
title = {Quenched mass transport of particles towards a target},
author = {Bruno Bouchard and Boualem Djehiche and Idris Kharroubi},
journal= {arXiv preprint arXiv:1707.07869},
year = {2018}
}