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 $\{X_n,n\geq 1\}$ be a sequence of i.i.d. random variables with partialsums $\{S_n,n\geq 1\}$. Based on the classical Baum-Katz theorem, a paper byHeyde in 1975 initiated the precise asymptotics for the sum $\sum_{n\geq1}\mbox{P}(|S_n|\geq\epsilon n)$ as $\epsilon$ goes to zero. Later, Klesovdetermined the convergence rate in Heyde's theorem. The aim of this paper is toextend Klesov's result to the precise asymptotics for Davis law of largenumbers, a theorem in Gut and Sp\u{a}taru [2000a].

Convergence rate in precise asymptotics for Davis law of large numbers