An almost sure invariance principle for the range of random walks
An almost sure invariance principle for the range of random walks
复制标题
随机游走范围的几乎确定的不变性原理
DOI：
10.1016/s0304-4149(98)00053-2
复制
发表时间：
1998
影响因子：
1.4
通讯作者：
Yuji Hamana
中科院分区：
文献类型：
--
作者：
Yuji Hamana
随机游走的范围是指在时间n之前随机游走至少访问过一次的不同站点的数量。本文研究了四维或多维整数格上随机游动值域的几乎必然不变性原理，得到了随机游动的中心化线性插值值域几乎必然渐近等于布朗运动.
The range of random walks means the number of distinct sites visited at least once by the random walk before time n. We study an almost sure invariance principle for the range of random walks on the four or more dimensional integer lattice and obtain that the centralized and linearly interpolated range of the random walk can be asymptotically equal to a Brownian motion almost surely.