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Fokker-Planck equations of jumping particles and mean field games of impulse control

Bertucci, Charles (2020), Fokker-Planck equations of jumping particles and mean field games of impulse control, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, 37, 5, p. 1211-1244. 10.1016/j.anihpc.2020.04.006

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Annales de l'Institut Henri Poincaré (C) Analyse non linéaire
Volume
37
Number
5
Publisher
Elsevier
Pages
1211-1244
Publication identifier
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Author(s)
Bertucci, Charles
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
This paper is interested in the description of the density of particles evolving according to some optimal policy of an impulse control problem. We first fix sets on which the particles jump and explain how we can characterize such a density. We then investigate the coupled case in which the underlying impulse control problem depends on the density we are looking for : the mean field games of impulse control. In both cases, we give a variational characterization of the densities of jumping particles.
Subjects / Keywords
mean field games of impulse control; jumping particles