Distribution dependent reflecting stochastic differential equations

To characterize the Neumann problem for nonlinear Fokker-Planck equations, we investigate distribution dependent reflecting stochastic differential equations (DDRSDEs) in a domain. We first prove the well-posedness and establish functional inequalities for reflecting stochastic differential equation...

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Bibliographic Details
Published in:	Science China. Mathematics Vol. 66; no. 11; pp. 2411 - 2456
Main Author:	Wang, Feng-Yu
Format:	Journal Article
Language:	English
Published:	Beijing Science China Press 01-11-2023 Springer Nature B.V
Subjects:	Applications of Mathematics Differential equations Fokker-Planck equation Mathematical analysis Mathematics Mathematics and Statistics Neumann problem Well posed problems 60H10 60G65 log-Harnack inequality well-posedness distribution dependent reflecting stochastic differential equations
Online Access:	Get full text
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Summary:	To characterize the Neumann problem for nonlinear Fokker-Planck equations, we investigate distribution dependent reflecting stochastic differential equations (DDRSDEs) in a domain. We first prove the well-posedness and establish functional inequalities for reflecting stochastic differential equations with singular drifts, and 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 stochastic differential equations is established.
ISSN:	1674-7283 1869-1862
DOI:	10.1007/s11425-021-2028-y