强相依高斯序列超过数点过程与部分和的联合渐近分布

JOINT ASYMPTOTIC DISTRIBUTIONS OF EXCEEDANCES POINT PROCESS AND PARTIAL SUM OF STRONG DEPENDENT GAUSSIAN SEQUENCES

｛Xn｝为标准化平稳高斯序列，pn＝EX1X（n＋1）.Nn为X1，X2，…Xn对水平的超过数形成的点过程，Mn（k）为X1，X2，Xn的第k个最大值，时，得到Nn与Sn、Mn（k）与Sn的联合渐近分布．

Let {Xn} be a standardized stationary Gaussian sequences, pn= EX1Xn＋1, Nn be the point process formed by the exceedances of level , M(k)n be the k-th largest maxima of X1, X2,…, Xn, The joint asymptotic distributions of Nn and Sn, M(k)n and Sn were derived under the condition pn log n→r ∈(0,∞).