论文标题
大象随机行走中心极限定理中的矩速率收敛速率
Rate of moment convergence in the central limit theorem for the elephant random walk
论文作者
论文摘要
一维大象随机步行是带有逐步加固的离散时间随机步行的典型模型，由Schütz和Trimper（2004）引入。它具有（-1,1）$：CASE $α= 0 $的参数$α\，对应于简单的对称随机步行，当$α> 0 $（resp。$α<0 $）时，walker time $ n $ grow（resp。vanisevanishes）的平均位移（例如$ n^α$）。步行将相位转变从$α= 1/2 $中，从扩散行为到超级延伸行为。在本文中，我们研究了$ -1 <α\ leq 1/2 $时，我们研究了中心极限定理中矩量定理的矩收敛速率。我们在$ m = 2,3，\ ldots $内部的200万美元的收敛速度上找到了一种交叉现象。
The one-dimensional elephant random walk is a typical model of discrete-time random walk with step-reinforcement, and is introduced by Schütz and Trimper (2004). It has a parameter $α\in (-1,1)$: The case $α=0$ corresponds to the simple symmetric random walk, and when $α>0$ (resp. $α<0$), the mean displacement of the walker at time $n$ grows (resp. vanishes) like $n^α$. The walk admits a phase transition at $α=1/2$ from the diffusive behavior to the superdiffusive behavior. In this paper, we study the rate of the moment convergence in the central limit theorem for the position of the walker when $-1 < α\leq 1/2$. We find a crossover phenomenon in the rate of convergence of the $2m$-th moments with $m=2,3,\ldots$ inside the diffusive regime $-1<α<1/2$.
