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.
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The author is grateful to the referee for valuable suggestions and to Professor Renming Song for helpful conversations.
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Wang, FY. Image-dependent conditional McKean–Vlasov SDEs for measure-valued diffusion processes. J. Evol. Equ. 21, 2009–2045 (2021). https://doi.org/10.1007/s00028-020-00665-z
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DOI: https://doi.org/10.1007/s00028-020-00665-z