标题： 伊藤-文策尔公式用于具有应用的半鞅条件分布的均场控制 显示英文标题

标题： Itô-Wentzell formulas for semimartingale conditional laws with applications to mean-field control

摘要： 本文是对Fadle-Touzi（2024）的扩展。 遵循相同的方法，仅基于泰勒展开，我们建立了广义半鞅条件分布流的伊藤公式和伊藤-文采尔公式，从而允许具有可能不连续的条件边缘流的不连续半鞅。 我们将这些结果应用于推导具有泊松型公共噪声的均值场控制问题的动态规划方程以及具有公共噪声的均值场停止问题的动态规划方程。 显示英文摘要

摘要： The present paper is an extension of Fadle-Touzi (2024). Following the same methodology, merely based on Taylor expansions, we establish the It\^o and It\^o-Wentzell formulae for flows of conditional distributions of general semimartingales, thus allowing for discontinuous semimartingales with possibly discontinuous flows of conditional marginals. We apply these results to derive the dynamic programming equations corresponding to mean field control problems with Poisson type common noise and mean field stopping problems with common noise.