We consider a special class of mean field SDEs with common noise which depends on the image of the solution (i.e., the conditional distribution given noise). The strong well-posedness is derived under a monotone condition which is weaker than those used in the literature of mean field games; the Feynman–Kac formula is established to solve Schrördinegr type PDEs on \(\mathscr {P}_2\), and the ergodicity is proved for a class of measure-valued diffusion processes.

中文翻译：

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基于图像的条件McKean-Vlasov SDE用于度量值扩散过程

我们考虑一类特殊的具有共同噪声的平均场SDE，它们取决于解的图像（即给定噪声的条件分布）。强的适定性是在单调条件下得出的，该条件比均值场博弈文献中所使用的弱。建立了Feynman–Kac公式来求解\（\ mathscr {P} _2 \）上的Schrördinegr型PDE ，并且证明了遍历性适用于一类具有测量值的扩散过程。