Joint Asymptotic Distributions of Exceedances Point Process and Partial Sum of Non-Stationary Gaussian Sequence

Let \X_i\^\infty_i=1 be a standardized non-stationary Gaussian sequence, and the exceedances point process N_n be the exceedances of level \mu_n(x) formed by X_1,X_2,\cdots,X_n, r_ij=\ep X_iX_j, S_n=\tsm_i=1^nX_i. Under some conditions, the asymptotic independence of N_n and S_n is obtained.