Originalversjon
Electronic Journal of Probability (EJP). 2022, 27 (none), 1-38, DOI: https://doi.org/10.1214/22-EJP756
Sammendrag
We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [17]. 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.