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 $\xi$ be an integrable random variable defined on $(\Omega, \mathcal{F},\mathbb{P})$. Fix $k\in \mathbb{Z}_+$ and let $\{\mathcal{G}_{i}^{j}\}_{1\le i\le n, 1\le j \le k}$ be a reference family of sub-$\sigma$-fields of$\mathcal{F}$, such that $\{\mathcal{G}_{i}^{j}\}_{1\le i \le n}$ is afiltration for each $j\in \{1,2,\dots,k\}$.  In this article we explain the underlying connection between the analysis ofthe maximal functions of the corresponding coherent vector and basiccombinatorial properties of the uncentered Hardy-Littlewood maximal operator.Following a classical approach of Grafakos, Kinnunen and Montgomery-Smith, weestablish an appropriate version of the celebrated Doob's maximal estimate.

Doob's estimate for coherent random variables and maximal operators on trees