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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we study the cut-off phenomenon under the total variationdistance of $d$-dimensional Ornstein-Uhlenbeck processes which are driven byL\'evy processes. That is to say, under the total variation distance, there isan abrupt convergence of the aforementioned process to its equilibrium, i.e.limiting distribution. Despite that the limiting distribution is not explicit,its distributional properties allow us to deduce that a profile function alwaysexists in the reversible cases and it may exist in the non-reversible casesunder suitable conditions on the limiting distribution. The cut-off phenomenafor the average and superposition processes are also determined.

Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by L\'evy processes