论文标题
随机步行的运行最大范围与小漂移
Bounds on the running maximum of a random walk with small drift
论文作者
论文摘要
我们得出了一个下限，因为可能是随机步行I.I.D. \增量，而小的负漂移$μ$超过了时间$ n $的值$ x> 0 $。当力矩生成函数以围绕原点的间隔界定时，该概率可以在下面以$ 1-O（x |μ| \ log n）$界定。该方法是基本的，不使用强近似定理。
We derive a lower bound for the probability that a random walk with i.i.d.\ increments and small negative drift $μ$ 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 $1-O(x|μ| \log N)$. The approach is elementary and does not use strong approximation theorems.
