Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ（n） =EX1Xn＋1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level （x/√2 l...Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ（n） =EX1Xn＋1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level （x/√2 log n＋√2 log n-log（4π log n）/2√log n） √1-τ（n） ＋ X^-n by X1,X2,…, Xn. Under some mild conditions, Nn and Sn are asymptotically independent, and Nn converges weakly to a Poisson process on （0,1].展开更多
In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically indepen...In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.展开更多
设{X_i}_(i=1)~∞是标准化强相依非平稳高斯序列,记S_n=sum from i=1 to n X_i,σ_n=(var(Sn))～(1/2)M_(t_n)~k为X_1,X_2,…,X_(t_n)的第k个最大值,N_(t_n)为X_1,X_2,…,X_(t_n)对水平μ_n(x)的超过数形成的点过程,t_n是一列单调增加...设{X_i}_(i=1)~∞是标准化强相依非平稳高斯序列,记S_n=sum from i=1 to n X_i,σ_n=(var(Sn))～(1/2)M_(t_n)~k为X_1,X_2,…,X_(t_n)的第k个最大值,N_(t_n)为X_1,X_2,…,X_(t_n)对水平μ_n(x)的超过数形成的点过程,t_n是一列单调增加的正整数列,在一定条件下得到N_(t_n)与S_n/σ_n,M_(t_n)~k与S_n/σ/n的联合渐近分布.展开更多
基金Supported by the Program for Excellent Talents in Chongqing Higher Education Institutions (120060-20600204)
文摘Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ（n） =EX1Xn＋1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level （x/√2 log n＋√2 log n-log（4π log n）/2√log n） √1-τ（n） ＋ X^-n by X1,X2,…, Xn. Under some mild conditions, Nn and Sn are asymptotically independent, and Nn converges weakly to a Poisson process on （0,1].
基金Supported by National Natural Science Foundation of China(Grant No.11171275)the Program for Excellent Talents in Chongqing Higher Education Institutions(Grant No.120060-20600204)supported by the Swiss National Science Foundation Project(Grant No.200021-134785)
文摘In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.
文摘设{X_i}_(i=1)~∞是标准化强相依非平稳高斯序列,记S_n=sum from i=1 to n X_i,σ_n=(var(Sn))～(1/2)M_(t_n)~k为X_1,X_2,…,X_(t_n)的第k个最大值,N_(t_n)为X_1,X_2,…,X_(t_n)对水平μ_n(x)的超过数形成的点过程,t_n是一列单调增加的正整数列,在一定条件下得到N_(t_n)与S_n/σ_n,M_(t_n)~k与S_n/σ/n的联合渐近分布.
