AI 中文总结
本文研究动态随机环境中每步以概率p完全重采样的随机游走，分析其极限速度v(p)的性质及极限扩散系数σ²(p)，得到相关极限定理。
AI 中文摘要
本文研究在动态随机环境中移动的随机游走，该环境在随机游走者每一步后以概率p完全重采样。这种重采样产生了直接的再生结构和极限定理，例如具有依赖于p的极限速度v(p)的大数定律。我们研究v(p)作为p的函数的若干性质，如可微性和单调性。类似地，我们研究中心极限定理中的极限扩散系数σ²(p)。
英文摘要
In this paper we consider random walks moving in a dynamic random environment that is completely resampled with probability $p$ after each step of the random walker. This resampling yields a straightforward regeneration structure and limit theorems, such as a law of large numbers with a limiting speed $v(p)$ that depends on $p$. We investigate several properties of $v(p)$ as a function of $p$, such as differentiability and monotonicity. Similarily, we study the limiting diffusivity $σ^2(p)$ in a central limit theorem.
Comments19 pages, 2 figures
