Abstract
The existence and uniqueness of stationary distributions and the exponential convergence in $ L^p $-Wasserstein distance are derived for SDEs driven by distribution dependent noise without uniformly dissipative drift. By using the exponential convergence and the Talagrand inequality of associated decoupled equations, global and local exponential convergences are established, and explicit convergence rate is obtained. Our results can be applied to the Curie-Weiss model and the granular media model in double-well landscape with quadratic interaction driven by distribution dependent noise.
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