标题： 关于大象随机游走的经典重对数律的备注 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： 本文研究了定义在$\mathbb{Z}$上的两个独立象随机游走（ERW），它们各自具有不同的记忆参数，能否无限次相遇的问题，扩展了 Roy、Takei 和 Tanemura 的工作。 我们还通过提供一个初等且易懂的证明，研究了它们之间距离的渐近行为，该证明涉及经典重对数律（LIL）在特定协方差核衰减条件下的中心化、连续、自相似高斯过程的应用。 显示英文摘要

摘要： This paper investigates whether two independent Elephant Random Walks (ERWs) on $\mathbb{Z}$, each with a different memory parameter, can meet infinitely often, extending the work of Roy, Takei, and Tanemura. We also study the asymptotic behavior of their distance by providing an elementary and accessible proof of the classical Law of the Iterated Logarithm (LIL) for centered, continuous, self-similar Gaussian processes under a certain decay condition on the covariance kernel.