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 depend 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 $\scr P_2$, and the ergodicity is proved for a class of measure-valued diffusion processes.

36 pages

References in corpus (2)

• From the master equation to mean field game limit theory: A central limit theorem
• Bismut Formula for Lions Derivative of Distribution Dependent SDEs and Applications