Image-dependent conditional McKean–Vlasov SDEs for measure-valued diffusion processes

Abstract

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.