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

Charles Bertucci

doi:10.1016/j.anihpc.2020.04.006

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

Charles Bertucci

Université Paris Dauphine

Research output: Contribution to journal › Article › peer-review

Abstract

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 the sets from 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 game of impulse control. In both cases, we give a variational characterization of the densities of jumping particles.

Original language	English
Pages (from-to)	1211-1244
Number of pages	34
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	37
Issue number	5
DOIs	https://doi.org/10.1016/j.anihpc.2020.04.006
Publication status	Published - 1 Sept 2020
Externally published	Yes

Keywords

Fokker-Planck equations
Impulse control
Mean field games
Partial differential equations

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10.1016/j.anihpc.2020.04.006

Cite this

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abstract = "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 the sets from 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 game of impulse control. In both cases, we give a variational characterization of the densities of jumping particles.",

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KW - Partial differential equations

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

Abstract

Keywords

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