论文标题
简单瞬态随机步行的复合泊松近似
Compound Poisson approximation for simple transient random walks in random sceneries
论文作者
论文摘要
给定一个简单的瞬态随机步行$（s_n）_ {n \ geq 0} $中的$ \ m athbf {z} $和一个真实随机变量的平稳序列$（ξ（s））_ {s {s \ in \ mathbf {z}} $，我们调查了序列$（s_n）的序列$（s_n）的极端。在适当的条件下，我们明确说明了极端指数，并表明超出点的点过程会收敛到复合泊松点过程。我们提供了两个示例，可以将群集大小分布明确。
Given a simple transient random walk $(S_n)_{n\geq 0}$ in $\mathbf{Z}$ and a stationary sequence of real random variables $(ξ(s))_{s\in \mathbf{Z}}$, we investigate the extremes of the sequence $(ξ(S_n))_{n\geq 0}$. Under suitable conditions, we make explicit the extremal index and show that the point process of exceedances converges to a compound Poisson point process. We give two examples for which the cluster size distribution can be made explicit.
