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In this paper, the strong existence and uniqueness for a degenerate finitesystem of quantile-dependent McKean-Vlasov stochastic differential equationsare obtained under a weak H\"{o}rmander condition. The approach relies on theapriori bounds for the density of the solution to time inhomogeneousdiffusions. The time inhomogeneous Feynman-Fac formula is used to construct acontraction map for this degenerate system.

Nonlinear McKean-Vlasov diffusions under the weak Hormander condition with quantile-dependent coefficients