论文标题
Wasserstein度量的指数收敛用于分布依赖性SDE
Exponential convergence in Wasserstein metric for distribution dependent SDEs
论文作者
论文摘要
固定分布的存在和唯一性以及$ l^p $ -Wasserstein距离中的指数收敛是从关联的解耦方程式的分布依赖性SDE中得出的。为了建立指数融合，我们引入了原始SDE和相关的分离方程的双重talagrand不平等，并获得了明确的收敛率。我们的结果可以应用于SDE，而无需均匀耗散的漂移和分布依赖性扩散项，该术语涵盖了Curie-Weiss模型，并以二孔相互作用为示例，涵盖了双孔景观中的颗粒介质模型。
The existence and uniqueness of stationary distributions and the exponential convergence in $L^p$-Wasserstein distance are derived for distribution dependent SDEs from associated decoupled equations. To establish the exponential convergence, we introduce a twinned Talagrand inequality of the original SDE and the associated decoupled equation, and explicit convergence rate is obtained. Our results can be applied to SDEs without uniformly dissipative drift and distribution dependent diffusion term, which cover the Curie-Weiss model and the granular media model in double-well landscape with quadratic interaction as examples.
