We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in . We provide several criteria for existence and uniqueness of solutions which go beyond the classical globally Lipschitz setting. In particular we show well-posedness of the equation, as well as almost sure convergence of the associated particle system, for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.
FH gratefully acknowledges financial support from the STORM project 274410, funded by the Research Council of Norway. LG is funded by the DFG under Germany’s Excellence Strategy – GZ 2047/1, project-id 390685813.
"Distribution dependent SDEs driven by additive continuous noise." Electron. J. Probab. 27 1 - 38, 2022. https://doi.org/10.1214/22-EJP756