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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.
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https://hal.archives-ouvertes.fr/hal-01567312
Contributor : Idris Kharroubi <>
Submitted on : Wednesday, October 31, 2018 - 9:31:13 AM
Last modification on : Friday, April 10, 2020 - 5:13:35 PM

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  • HAL Id : hal-01567312, version 2
  • ARXIV : 1707.07869

Citation

Bruno Bouchard, Boualem Djehiche, Idris Kharroubi. Quenched mass transport of particles towards a target. 2017. ⟨hal-01567312v2⟩

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