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

Given a super-critical Galton-Watson process $\{Z_n\}$ and a positivesequence $\{\epsilon_n\}$, we study the limiting behaviors of$P(S_{Z_n}/Z_n\geq\epsilon_n)$ and $P(S_{Z_n}/m^n\geq\epsilon_n) $ with sums$S_{n}$ of i.i.d. random variables $X_i$ and $m=E[Z_1]$. We assume that we arein Schr\"oder case with $EZ_1\log Z_1<\infty$ and $X_1$ is in the domain ofattraction of an $\alpha$-stable law with $0<\alpha<2$. As by-products, when$Z_1$ is sub-exponentially distributed, we further obtain the convergence ratesof $ \frac{Z_{n+1}}{Z_n}$ to $m$ as $n\rightarrow\infty$.

On large deviation rates for sums associated with Galton-Watson processes