Theory of Probability &Its Applications, Volume 67, Issue 2, Page 294-309, August 2022.
This note is devoted to the study of the maximum of the excursion of a random walk with negative drift and light-tailed increments. More precisely, we determine the local asymptotics of the joint distribution of the length, the maximum, and the time at which this maximum is achieved. This result allows one to obtain a local central limit theorem for the length of the excursion conditioned on large values of the maximum.

中文翻译：

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随机游走偏移长度和最大值联合分布的局部尾渐近

概率理论及其应用，第 67 卷，第 2 期，第 294-309 页，2022 年 8 月
。本说明致力于研究具有负漂移和轻尾增量的随机游走的最大偏移。更准确地说，我们确定了长度、最大值和达到该最大值的时间的联合分布的局部渐近线。这一结果允许人们获得以最大值为条件的偏移长度的局部中心极限定理。