孙鸿雁, 王华明. 半直线格点上随机游动的最大值[J]. 应用概率统计, 2023, 39(5): 633-642. DOI: 10.3969/j.issn.1001-4268.2023.05.001
引用本文: 孙鸿雁, 王华明. 半直线格点上随机游动的最大值[J]. 应用概率统计, 2023, 39(5): 633-642. DOI: 10.3969/j.issn.1001-4268.2023.05.001
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SUN Hongyan, WANG Huaming. On a Maximum of Some Random Walk on Lattice of Half Line[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(5): 633-642. DOI: 10.3969/j.issn.1001-4268.2023.05.001
Citation: SUN Hongyan, WANG Huaming. On a Maximum of Some Random Walk on Lattice of Half Line[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(5): 633-642. DOI: 10.3969/j.issn.1001-4268.2023.05.001
shu

半直线格点上随机游动的最大值

On a Maximum of Some Random Walk on Lattice of Half Line

    摘要
  • 摘要: 本文研究半直线上带渐近零漂移的紧邻随机游动.用M表示从1到0的一个游程内粒子的最大位置. 本文研究M的分布,并刻划它的渐近分布, 该结果与简单随机游动不同.

     

    Abstract: Consider a nearest-neighbor random walk with certain asymptotically zero drift on the positive half line. Let M be the maximum of an excursion starting from 1 and ending at 0. We study the distribution of M and characterize its asymptotics, which is quite different from those of simple random walks.

     

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