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In June 2012 on a conference in Bielefeld, after the author made thepresentation of his theory of nonlinear Markov processes, Tom Kurtz asked himwhether his methods would allow to get well-posedness for nonlinearMcKean-Vlasov type diffusions with coefficients depending on the distributionvia the median. The present paper is the answer to this question. The aim hereis not to find the weakest possible conditions for the affirmative answer, buta sensible general result with a quick and transparent proof.

Nonlinear diffusions and stable-like processes with coefficients depending on the median or VaR