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We study distribution dependent stochastic differential equation driven by acontinuous process, without any specification on its law, following theapproach initiated in [16]. We provide several criteria for existence anduniqueness of solutions which go beyond the classical globally Lipschitzsetting. In particular we show well-posedness of the equation, as well asalmost sure convergence of the associated particle system, for driftssatisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolevdifferentiability type assumptions.

Distribution dependent SDEs driven by additive continuous noise