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Distribution dependent reflecting stochastic differential equations

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Abstract

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.

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Acknowledgements

This work was supported by the National Key R&D Program of China (Grant No. 2020YFA0712900) and National Natural Science Foundation of China (Grant Nos. 11831014 and 11921001). The author thanks Bin Xie, Xing Huang, Shen Wang, Wei Hong, Bingyao Wu, Shanshan Hu and the referees for their helpful comments and corrections to earlier versions of the paper.

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  1. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China

    Feng-Yu Wang

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  1. Feng-Yu Wang
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Correspondence to Feng-Yu Wang.

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Wang, FY. Distribution dependent reflecting stochastic differential equations. Sci. China Math. 66, 2411–2456 (2023). https://doi.org/10.1007/s11425-021-2028-y

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