English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $(X_t)_{t \geq 0}$ be a diffusion process defined on a compact Riemannianmanifold, and for $\alpha > 0$, let $$ \mu_t^{(\alpha)} =\frac{\alpha}{t^\alpha} \int_{0}^{t} \delta_{X_s} \, s^{\alpha - 1} \mathrm{d}s $$ be the associated weighted empirical measure. We investigate asymptoticbehavior of $\mathbb{E}^\nu \big[ \mathrm{W}_2^2(\mu_t^{(\alpha)}, \mu) \big]$for sufficient large $t$, where $\mathrm{W}_2$ is the quadratic Wassersteindistance and $\mu$ is the invariant measure of the process. In the particularcase $\alpha = 1$, our result sharpens the limit theorem achieved in [26]. Theproof is based on the PDE and mass transportation approach developed by L.Ambrosio, F. Stra and D. Trevisan.

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