Distribution Dependent Reflecting Stochastic Differential Equations

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.

58 pages

References in corpus (2)

• Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
• Strong Solutions to Reflecting Stochastic Differential Equations with Singular Drift