Distribution Dependent Reflecting Stochastic Differential Equations

TL;DR

This paper studies distribution-dependent reflecting stochastic differential equations (SDEs) in bounded domains, establishing well-posedness and functional inequalities, and extending results to equations with singular or monotone coefficients.

Contribution

It introduces a general criterion linking the well-posedness of distribution-dependent reflecting SDEs to that of classical reflecting SDEs, including cases with singular or monotone coefficients.

Findings

Proved well-posedness of reflecting SDEs with singular drifts.

Extended well-posedness results to distribution-dependent reflecting SDEs.

Established functional inequalities for these SDEs.

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.