Buraczewski Dariusz, Dyszewski Piotr, Iksanov Alexander, Marynych Alexander, Roitershtein Alexander
Mathematical Institute, University of Wroclaw, 50-384 Wroclaw, Poland.
Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine.
Electron J Probab. 2019;24. doi: 10.1214/19-EJP330. Epub 2019 Jun 28.
A random walk in a sparse random environment is a model introduced by Matzavinos et al. [Electron. J. Probab. 21, paper no. 72: 2016] as a generalization of both a simple symmetric random walk and a classical random walk in a random environment. A random walk in a sparse random environment is a nearest neighbor random walk on that jumps to the left or to the right with probability 12 from every point of and jumps to the right (left) with the random probability λ (1 - λ ) from the point , . Assuming that are independent copies of a random vector and the mean is finite (moderate sparsity) we obtain stable limit laws for , properly normalized and centered, as → . While the case ≤ a.s. for some deterministic > 0 (weak sparsity) was analyzed by Matzavinos et al., the case (strong sparsity) will be analyzed in a forthcoming paper.
稀疏随机环境中的随机游走是Matzavinos等人[《电子概率杂志》21卷，第72号论文：2016年]引入的一个模型，它是简单对称随机游走和随机环境中经典随机游走的一种推广。稀疏随机环境中的随机游走是在 上的最近邻随机游走，从 的每个点以概率 1/2 向左或向右跳跃，并从点 以随机概率 λ (1 - λ ) 向右（左）跳跃。假设 是随机向量 的独立副本，且均值 是有限的（适度稀疏），当 → 时，对于经过适当归一化和中心化的 ，我们得到了稳定的极限律。虽然对于某个确定性的 > 0， ≤ 几乎必然成立（弱稀疏）的情况已由Matzavinos等人进行了分析，但 （强稀疏）的情况将在即将发表的论文中进行分析。
