Distribution dependent SDEs driven by additive continuous noise

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.

Automated summary

This article studies distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [17]. Several criteria for existence and uniqueness of solutions beyond the classical globally Lipschitz setting are provided. In particular, well-posedness of the equation and almost sure convergence of the associated particle system are shown for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.