论文标题
在大象随机步行中，停止玩捉迷藏和寻找米塔格 - leffler发行
On the elephant random walk with stops playing hide and seek with the Mittag-Leffler distribution
论文作者
论文摘要
本文的目的是研究所谓的大象随机行走的渐近行为（ERWS）。与标准的大象随机步行相反，大象可以保持自己的位置懒惰。我们证明，正确标准化的ERW的数量几乎可以融合到Mittag-Leffler分布。它使我们能够对ERWS的渐近行为进行尖锐的分析。在扩散和关键的制度中，我们建立了ERWS几乎确定的融合。我们还表明，有必要通过随机数来自称ERW的位置，以证明渐近正态性。在超级未来的制度中，我们建立了适当标准化的ERW的几乎确定的收敛，将其与非排定随机变量相关。此外，我们还表明，ERW在其限制随机变量周围的波动仍然是高斯。
The aim of this paper is to investigate the asymptotic behavior of the so-called elephant random walk with stops (ERWS). In contrast with the standard elephant random walk, the elephant is allowed to be lazy by staying on his own position. We prove that the number of ones of the ERWS, properly normalized, converges almost surely to a Mittag-Leffler distribution. It allows us to carry out a sharp analysis on the asymptotic behavior of the ERWS. In the diffusive and critical regimes, we establish the almost sure convergence of the ERWS. We also show that it is necessary to self-normalized the position of the ERWS by the random number of ones in order to prove the asymptotic normality. In the superdiffusive regime, we establish the almost sure convergence of the ERWS, properly normalized, to a nondegenerate random variable. Moreover, we also show that the fluctuation of the ERWS around its limiting random variable is still Gaussian.
