强相依平稳正态序列最大值和最小值的联合极限分布

On the joint limiting distribution of the maximum and minimum of strong dependent stationary normal sequence

设X 1,X 2,是标准化的平稳正态序列,M n=m1≤ia≤xnXi,mn=m1≤ii≤nnXi,ρn=EX 1 Xn+1 Rn=M n-mn,

Let X1, X2... be standardized stationary normal sequence, Mn=maxISiSnXi,mn=minXiISiSn,Pn=EX1Xn＋1 Rn=Mn-mn,Sn=n∑i=1Xi,Suppose that po and （pn logn）^-1 both are monotone and converging to zero, the joint limiting distribution of Mn and mn is derived, so is Rn . At the same time, we can obtain the joint limiting distribution of Mn, mn and Sn.