摘要
设X(t)=(X_1(t),…,X_r(t)),t≥0是一个r维(严)平稳过程,对任何区间I,令M_i(I)=sup{X_i(t):t∈I},1≤i≤r,M(I)=(M_1(I),…,M_r(I))。如果I=[0,T],则记M_i([0,T])=M_i(T),1≤i≤r,M([0,T])=M(T)。本文总是假定对每个1≤i≤r,X_i(t)有连续的一维分布,且样本函数以概率1连续。还假定基本概率空间是完全的。因此,对任何区间I,M(I)是随机向量。
Let X(t)=(X_1(t),…,X_t(t)),t≥0 be an r-dimesional continuous parameter stationary process,M_i(T)=sup{X_i(t):0≤t≤T},i=1,…,rM(T)=(M_1(T),…,M_r(T)),T≥0.In this paper,we obtain the asymptotic distribution for M(T) and a sufficient and necessary condition for the independence of M_1(T),…,M_r(T) under appropriate dependence restrictions.The asymptotic independence of point processes of upcrossings of high levels by stationary processes X_i(t),i=1,…,r is established.
出处
《应用数学学报》
CSCD
北大核心
1991年第4期549-561,共13页
Acta Mathematicae Applicatae Sinica
