| 张美娟.随机环境中分枝随机游动的极限定理[J].数学年刊A辑,2013,34(6):727~736 |
| 随机环境中分枝随机游动的极限定理 |
| Limit Theorems for Branching Random Walk in a Random Environment |
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| DOI： |
| 中文关键词: 随机环境中的分枝随机游动, Annealed, Harris 猜想, 中心极限定理 |
| 英文关键词:Branching random walk in a random environment, Annealed,
Harris’ conjecture, Central limit theorem |
| 基金项目:国家自然科学基金 (No.11131003) |
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| 中文摘要: |
| 假定环境平稳遍历, 考虑随机环境中的分枝随机游动. 在此模型中, 粒子以上临界的Galton-Watson 过程分枝产生后代, 而以一维紧邻随机环境中的随机游动进行运动. 令~$Z_{n}(B)$ 表示时间~$n$ 落于~$B$ 中的粒子数, 其中~$B$ 为~$\mathbb{R}$ 中任一子集. 得到了计数测度~$Z_{n}(\cdot)$ 经过适当的规范化之后, 在~``annealed" 情形下的中心极限定理. |
| 英文摘要: |
| Consider a model of branching random walk in a random environment, where the particles reproduce as a supercritical Galton-Watson process with a fixed reproduction law, but move as a nearest neighbor random walk on $\mathbb{Z}$ in a stationary and ergodic random environment. For $B\subset \mathbb{R}$, let $Z_{n}(B)$ be the number of particles of generation $n$ located in $B$. The author obtains central limit theorems for the counting measure $Z_{n}(\cdot)$ with appropriate normalization in the annealed case. |
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