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

We study the effect of approximation errors in assessing the extremebehaviour of univariate functionals of random objects. We build our frameworkinto a general setting where estimation of the extreme value index and extremequantiles of the functional is based on some approximated value instead of thetrue one. As an example, we consider the effect of discretisation errors incomputation of the norms of paths of stochastic processes. In particular, wequantify connections between the sample size $n$ (the number of observedpaths), the number of the discretisation points $m$, and the modulus ofcontinuity function $\phi$ describing the path continuity of the underlyingstochastic process. As an interesting example fitting into our framework, weconsider processes of form $Y(t) = \mathcal{R}Z(t)$, where $\mathcal{R}$ is aheavy-tailed random variable and the increments of the process $Z$ have lightertails compared to $\mathcal{R}$.

Hill estimator and extreme quantile estimator for functionals of approximated stochastic processes