论文标题
在随机风景中随机步行的超出点过程
Point processes of exceedances for random walks in random sceneries
论文作者
论文摘要
令$ \ {ξ（k），k \ in \ mathbb {z} \} $为随机变量的固定顺序，让$ \ {s_n，n \ in \ mathbb {n} _+ \ \} $在稳定法律的吸引力范围内暂时随机行走。在以前的工作中\ cite {nicolas_ahmad}，在类型$ d（u_n）$和$ d'（u_n）$的条件下，我们为序列$ \ {ξ（s_n），n \ in \ mathbb {n} \} $的第一个$ n $条款的最大值提供了一个限制定理。在本文中，在相同的条件下，我们将看到，计算出$ \ {ξ（s_k）> u_n \}表格超出数量的过程的限制，k \ geq 1 $是复合泊松点过程。我们还处理了序列$ \ {ξ（s_n），n \ in \ mathbb {n} \} $的所谓极端索引，我们讨论了一些弱混合属性。
Let $\{ξ(k), k \in \mathbb{Z} \}$ be a stationary sequence of random variables and let $\{S_n, n \in \mathbb{N}_+ \}$ be a transient random walk in the domain of attraction of a stable law. In the previous work \cite{Nicolas_Ahmad}, under conditions of type $D(u_n)$ and $D'(u_n)$ we provided a limit theorem for the maximum of the first $n$ terms of the sequence $\{ξ(S_n), n \in \mathbb{N} \}$. In this paper, under the same conditions we will see that, the limit of the process which counts the numbers of the exceedances of the form $\{ξ(S_k)>u_n\}, k\geq 1$, is a compound Poisson point process. We also deal with the so-called extremal index for the sequence $\{ξ(S_n), n \in \mathbb{N} \}$ and we discuss some weak mixing properties.
