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.

中文翻译：

---

跳跃粒子的Fokker-Planck方程和脉冲控制的均值场博弈

本文对根据冲量控制问题的一些最佳策略发展的粒子密度的描述感兴趣。我们首先确定粒子跳出的位置，并说明如何表征这种密度。然后，我们研究耦合的情况，其中潜在的脉冲控制问题取决于我们正在寻找的密度：脉冲控制的均值现场博弈。在这两种情况下，我们都给出了跳跃粒子密度的变化特征。