强相依非平稳序列上超点过程的收敛性

{ξi,i≥1}为标准化的正态序列,rij=Cov(ξi,ξj)。M(nk)是{ξi,i≥1}第k个最大值,本文在条件:j-i→∞时r■log(j-i)→γ∈(0,∞)下,得到了ξ1,ξ2,…,ξn时间正规化上超水平u(n1),u(n2),…,u(n)r形成的点过程依分布收敛到定义在(0,+∞)×R上的二维Cox-过程。

On the Convergence of the Process of Exceedances by Strongly Non-stationary Sequences

Let {ξi,i≥1} be a standard normal sequences.M is the k th maximum.In the paper,under the condition r■log(j-i)→γ∈(0,∞)as j-i→∞,we obtained the point process of time-normalized exceedances of levels u,u,…,u converges in distribution to Cox-process on the entire right half plane,i.e.on(0,+∞)×R.