标题： 关于基于经典重对数律的随机游走象的注记 显示英文标题

标题： A remark on elephant random walks via the classical law of the iterated logarithm for self-similar Gaussian processes

摘要： 本文的主要关注点是研究定义在$\mathbb{Z}$上具有不同记忆参数的两个大象随机游走（ERW）是否可以无限次地相遇的问题，推广了 Roy、Takei 和 Tanemura 的结果。 我们还通过提供一个初等且易懂的经典重对数律（LIL）的证明，研究了它们之间的距离的渐近行为，该证明适用于中心化的连续自相似高斯过程，并在协方差核满足某种衰减条件下进行了分析。 显示英文摘要

摘要： The main concern of this paper is to investigate the problem whether two Elephant Random Walks (ERWs) on $\mathbb{Z}$ with different memory parameters can meet each other infinitely often, extending the result by Roy, Takei, and Tanemura. We also study the asymptotic behavior of the distance between them by providing an elementary and accessible proof of the classical Law of Iterated Logarithm (LIL) for centered continuous self-similar Gaussian processes under a certain decay condition on the covariance kernel.