# State-Density Flows of Non-Degenerate Density-Dependent Mean Field SDEs and Associated PDEs

@inproceedings{Huang2021StateDensityFO, title={State-Density Flows of Non-Degenerate Density-Dependent Mean Field SDEs and Associated PDEs}, author={Ziyuan Huang and Shanjian Tang}, year={2021} }

In this paper, we study a combined system of a Fokker-Planck (FP) equation for m with initial (t, μ) ∈ [0, T ] × L(R), and a stochastic differential equation (SDE) for X with initial (t, x) ∈ [0, T ] × R, whose coefficients depend on the solution of FP equation. We develop a combined probabilistic and analytical method to explore the regularity of the functional V (t, x, μ) = E[Φ(X T ,m (T, ·))]. Our main result states that, under a nondegenerate condition and appropriate regularity assumptions…

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