Quenched Mass Transport of Particles Toward a Target

Bruno Bouchard (), Boualem Djehiche and Idris Kharroubi ()
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Bruno Bouchard: Université Paris-Dauphine, PSL University, CNRS
Idris Kharroubi: Sorbonne Université, Université de Paris

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 2, No 1, 345-374

Abstract: 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. This kind of problems is motivated by limiting behavior of interacting particles systems with applications in, for example, agricultural crop management. 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 toward a given target, along the paths of a stochastic differential equation. Our results extend those of Soner and Touzi, Journal of the European Mathematical Society (2002) to our setting.

Keywords: McKean–Vlasov SDEs; Dynamic programming; Stochastic target; Mass transportation; Viscosity solutions; 93E20; 60K35; 49L25 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-020-01704-y

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