Asymptotic behavior of Wasserstein distance for weighted empirical measures of diffusion processes on compact Riemannian manifolds

Jie-Xiang Zhu

Let $(X_t{)}_{t\ge 0}$ be a diffusion process defined on a compact Riemannian manifold, and for $\alpha >0$, let $$ μ_t^{(α)} = \fracα{t^α} \int_{0}^{t} δ_{X_s} \, s^{α- 1} \mathrm{d} s…