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/

Zendy Plus

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

Zendy Tools

Zendy Open

We derive uniform concentration inequalities for continuous-time analogues ofempirical processes and related stochastic integrals of scalar ergodicdiffusion processes. Thereby, we lay the foundation typically required for thestudy of sup-norm properties of estimation procedures for a large class ofdiffusion processes. In the classical i.i.d. context, a key device for thestatistical sup-norm analysis is provided by Talagrand-type concentrationinequalities. Aiming for a parallel substitute in the diffusion framework, wepresent a systematic, self-contained approach to such uniform concentrationinequalities via martingale approximation and moment bounds obtained by thegeneric chaining method. The developed machinery is of independentprobabilistic interest and can serve as a starting point for investigations ofother processes such as more general Markov processes, in particularmultivariate or discretely observed diffusions. As a first concrete statisticalapplication, we analyse the sup-norm error of estimating the invariant densityof an ergodic diffusion via the natural local time estimator and the classicalnonparametric kernel density estimator, respectively.

Concentration of scalar ergodic diffusions and some statistical implications