Limit Theorems for Random Walks in Symmetric Random Environments
Limit Theorems for Random Walks in Symmetric Random Environments
复制标题
对称随机环境中随机游走的极限定理
DOI：
10.1137/1129037
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发表时间：
1985
影响因子：
0.6
通讯作者：
A. O. Golosov
中科院分区：
文献类型：
--
作者：
A. O. Golosov
1.通过随机游走，我们将意指具有状态空间Z {.，l，0，l，.}，初始状态0，强度转变a（x，y）从x Z到y Z。转变强度的集合{（x，y）：x，y Z}将被称为其中发生行走的介质。设XRc ′ 1是其路的空间，x是由X的柱面子集生成的代数.在可测空间（X，x）上对应于随机游走的分布将由Pa表示。设是所有可能环境的集合，设ff是由c z 2的柱面子集生成的tr-代数。我们假设a（x，y）是随机变量，其分布由（，）上的某个分布给出。
1. By a random walk, we shall mean a homogeneous Markov process with state space Z {., l, 0, l,.}, initial state 0, intensity transitions a (x, y) from x Z to y Z. The set of transition intensities{(x, y): x, y Z} will be referred to as the medium in which the walk takes place. Let XRc’l be the space of paths of the walk, and let xbe thetr-algebra generated by the cylinder subsets of X. A distribution on the measurable space (X, x) corresponding to a random walk in will be denoted by Pa. Let be the set of all possible environments and let ff be the tr-algebra generated by the cylinder subsets of c z2. We assume that the a (x, y) are random variables whose distribution is given by some distribution on (,).