论文标题
大象随机步行的cramér中度偏差
Cramér moderate deviations for the elephant random walk
论文作者
论文摘要
我们为一维大象随机步行建立了一些限制定理，包括浆果 - 埃斯尼界，cramér中度偏差和局部极限定理。这些极限定理可以被视为大象随机行走的中心极限定理的改进。此外，按照这些限制定理，我们得出结论，正态分布的吸引力领域主要取决于内存参数$ p $，该$ p $位于$ 0 $和3/4. $之间。
We establish some limit theorems for one-dimensional elephant random walk, including Berry-Esseen bounds, Cramér moderate deviations and local limit theorems. These limit theorems can be regarded as refinements of the central limit theorems for the elephant random walk. Moreover, by these limit theorems, we conclude that the domain of attraction of normal distribution mainly depends on a memory parameter $p$ which lies between $0$ and $3/4.$
