Central Limit Theorem for Linear Stochastic Evolutions
Central Limit Theorem for Linear Stochastic Evolutions
复制标题
线性随机演化的中心极限定理
DOI：
10.1215/kjm/1248983037
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发表时间：
2009
影响因子：
--
通讯作者：
M. Nakashima
中科院分区：
文献类型：
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作者：
M. Nakashima
我们考虑一个值为 [0,$\infty$)$^{\mathbb{z}d}$ 的马尔可夫链。马尔可夫链包括一些有趣的例子，例如定向位点渗透、随机环境中的定向聚合物以及二元接触过程的时间离散。当 $d\geq 3$ 和总人口的某个平方可积条件满足时，我们证明了“人口空间分布”的中心极限定理。这将随机环境中定向聚合物的已知结果扩展到一大类模型。
We consider a Markov chain with values in [0,$\infty$)$^{\mathbb{z}d}$. The Markov chain includes some interesting examples such as the oriented site percolation, the directed polymers in random environment, and a time discretization of the binary contact process. We prove a central limit theorem for �the spatial distribution of population� when $d\geq 3$ and a certain square-integrability condition for the total population is satisfied. This extends a result known for the directed polymers in random environment to a large class of models.