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

In this article we refine well-known results concerning the fluctuations ofone-dimensional random walks. More precisely, if $(S_n)_{n \geq 0}$ is a randomwalk starting from 0 and $r\geq 0$, we obtain the precise asymptotic behavioras $n\to\infty$ of $\mathbb P[\tau^{>r}=n, S_n\in K]$ and $\mathbbP[\tau^{>r}>n, S_n\in K]$, where $\tau^{>r}$ is the first time that the randomwalk reaches the set $]r,\infty[$, and $K$ is a compact set. Our assumptions onthe jumps of the random walks are optimal. Our results give an answer to aquestion of Lalley stated in [9], and are applied to obtain the asymptoticbehavior of the return probabilities for random walks on $\mathbb R^+$ withnon-elastic reflection at 0.

Some aspects of fluctuations of random walks on R and applications to random walks on R+ with non-elastic reflection at 0