具有小漂移的随机漫步的运行最大值的边界

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-10-17 DOI:10.30757/alea.v19-03

Ofer Busani, T. Seppalainen

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引用次数: 2

摘要

我们推导了一个概率的下界，即具有i.i.d增量和小负漂移$\mu$的随机漫步在时间$N$上超过$x>0$的值。当矩生成函数在原点附近的一个区间内有界时，这个概率可以用$1-O(x|\mu| \log N)$为界。该方法是初等的，不使用强逼近定理。

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Bound on the running maximum of a random walk with small drift

We derive a lower bound for the probability that a random walk with i.i.d.\ increments and small negative drift $\mu$ exceeds the value $x>0$ by time $N$. When the moment generating functions are bounded in an interval around the origin, this probability can be bounded below by $1-O(x|\mu| \log N)$. The approach is elementary and does not use strong approximation theorems.

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来源期刊

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.