非平稳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 Non-Stationary Gaussian Sequence

摘要: 设\X_i\^\infty_i=1是标准化非平稳高斯序列, N_n为X_1,X_2,\cdots,X_n对水平\mu_n(x)的超过数形成的点过程, r_ij=\ep X_iX_j, S_n=\tsm_i=1^nX_i. 在r_ij满足一定条件时, 本文得到了N_n与S_n的渐近独立性.

Abstract: 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.