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

Let {Xk : k = 1, 2,... } be a sequence of random variables with zero mean and finite variance <7^. We say that {Xk} is blockwise m-dependent if for each p large enough the following is true: if we remove m or more consec- utive X's from the dyadic block {X2p-1 +1,..., AT2P }, then the two remaining portions are independent. We say that {Xk} is blockwise quasiorthogonal if for each p, the expectations E(XkXi) are small in a certain sense again within the dyadic block {X2P-1+1,..., X2P }. Blockwise independence and blockwise orthogonality are particular cases of the above notions, respectively. We study the a.s. behavior of the series 2~2k-i ^k an<^ *^a* °^ ^e ^rs* arithmetic means (1/n) ?~2k_, Xk. It turns out that the classical strong limit theorems, with one exception, remain valid in this more general setting, too.

Strong limit theorems for blockwise 𝑚-dependent and blockwise quasi-orthogonal sequences of random variables