论文标题
一维简单随机步行的最喜欢的下跨站点
Favorite Downcrossing Sites of One-Dimensional Simple Random Walk
论文作者
论文摘要
随机步行是一个非常重要的马尔可夫过程，并且在许多领域中都有重要的应用程序。对于一维简单的对称随机步行$（s_n）$，如果其在时间$ n $的下降时间$ n $在所有站点中达到最高最高的时间$ n $，则将$ x $称为最喜欢的时间$ n $。在本文中，我们研究了最喜欢的下越交站点集的基数，并将表明概率1只有有限的次数至少有四个最喜欢的下跨站点和三个最喜欢的下层面地点经常出现。将引入一些相关的开放问题。
Random walk is a very important Markov process and has important applications in many fields.For a one-dimensional simple symmetric random walk $(S_n)$, a site $x$ is called a favorite downcrossing site at time $n$ if its downcrossing local time at time $n$ achieves the maximum among all sites. In this paper, we study the cardinality of the favorite downcrossing site set, and will show that with probability 1 there are only finitely many times at which there are at least four favorite downcrossing sites and three favorite downcrossing sites occurs infinitely often. Some related open questions will be introduced.
