Distribution Dependent Reflecting Stochastic Differential Equations

Feng-Yu Wang

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arXiv · 2106.12737

Distribution Dependent Reflecting Stochastic Differential Equations

Feng-Yu Wang

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Abstract

To characterize the Neumann problem for nonlinear Fokker-Planck equations, we investigate distribution dependent reflecting SDEs (DDRSDEs) in a domain. We first prove the well-posedness and establish functional inequalities for reflecting SDEs with singular drifts, then extend these results to DDRSDEs with singular or monotone coefficients, for which a general criterion deducing the well-posedness of DDRSDEs from that of reflecting SDEs is established.

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Feng-Yu Wang. 2021-06-24. Distribution Dependent Reflecting Stochastic Differential Equations. https://arxiv.org/abs/2106.12737

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