期刊论文详细信息
Electronic Communications in Probability | |
On the ladder heights of random walks attracted to stable laws of exponent 1 | |
Kôhei Uchiyama1 | |
关键词: random walk; stable law of exponent 1; domain of attraction; slowly varying; ladder height; large deviation; | |
DOI : 10.1214/18-ECP122 | |
学科分类:统计和概率 | |
来源: Institute of Mathematical Statistics | |
【 摘 要 】
Let $Z$ be the first ladder height of a one dimensional random walk $S_n=X_1+\cdots + X_n$ with i.i.d. increments $X_j$ which are in the domain of attraction of a stable law of exponent $\alpha $, $0x]$ is slowly varying at infinity if and only if $\lim _{n\to \infty } n^{-1}\sum _1^n P[S_k>0]=0$. By a known result this provides a criterion for $S_{T(R)} /R \stackrel{{\rm P}} \longrightarrow \infty $ as $R\to \infty $, where $T(R)$ is the time when $S_n$ crosses over the level $R$ for the first time. The proof mostly concerns the case $\alpha =1$.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO201910283070359ZK.pdf | 303KB | download |