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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

By using the spectrum of the underlying symmetric diffusion operator, theconvergence in $L^p$-Wasserstein distance $\mathbb W_p (p\ge 1)$ ischaracterized for the empirical measure $\mu_t$ of non-symmetric subordinateddiffusion processes in an abstract framework. The main results are applied tothe subordinations of several typical models, which include the (reflecting)diffusion processes on compact manifolds, the conditional diffusion processes,the Wright-Fisher diffusion process, and hypoelliptic diffusion processes on{\bf SU}(2). In particular, for the (reflecting) diffusion processes on acompact Riemannian manifold with invariant probability measure $\mu$:  (1) the sharp limit of $t\mathbb W_2(\mu_t,\mu)^2$ is derived in $L^q(\mathbbP)$ for concrete $q\ge 1,$ which provides a precise characterization on thephysical observation that a divergence-free perturbation accelerates theconvergence in $\mathbb W_2$;  (2) the sharp convergence rates are presented for $(\mathbb E[\mathbbW_{2p}(\mu_t,\mu)^{q}])^{\frac 1 q} (p,q\ge 1)$, where a critical phenomenonappears with the critical rate $t^{-1}\log t$ as $t\to\infty$.

Convergence in Wasserstein Distance for Empirical Measures of Non-Symmetric Subordinated Diffusion Processes