Distribution Dependent Reflecting Stochastic Differential Equations
arXiv:2106.12737
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.
arXiv comment58 pages
References in corpus (6)
- Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
- Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds
- Large Deviations and Exit-times for reflected McKean-Vlasov equations with self-stabilizing terms and superlinear drifts
- A Zvonkin's transformation for stochastic differential equations with singular drift and related applications
- Strong Solutions to Reflecting Stochastic Differential Equations with Singular Drift
- Exponential Ergodicity for Singular Reflecting McKean-Vlasov SDEs