Tan, Zhongquan; Peng, Zuoxiang Joint asymptotic distribution of exceedances point processes and partial sums of strong dependent non-stationary Gaussian sequences. (Chinese. English summary) Zbl 1240.60135 Acta Math. Appl. Sin. 34, No. 1, 24-32 (2011). Summary: Let \(\{X_i\}^\infty_{i=1}\) be a standardized strong dependent non-stationary Gaussian sequence, and \(N_{t_n}\) be a point process of exceedances of level \(\mu_n (x)\) by \(X_1, X_2, \cdots, X_{t_n},\;S_n=\sum\limits^n_{i=1}X_i,\sigma_n=\sqrt{\text{var} (S_n)}, M^k_{t_n}\) be the \(k\)-th largest maxima of \(X_1, X_2, \cdots, X_{t_n}\), where \(t_n\) is a sequence of increasing positive integer numbers. Under some conditions, the joint asymptotic distribution functions of \(N_n\) and \(\frac{S_n}{\sigma_n}, M^k_{t_n}\) and \(\frac{S_n}{\sigma_n}\) are obtained. Cited in 1 Document MSC: 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 60G70 Extreme value theory; extremal stochastic processes 60G15 Gaussian processes Keywords:strong dependent non-stationary Gaussian sequence; the exceedances point process; partial sum; Cox-process PDFBibTeX XMLCite \textit{Z. Tan} and \textit{Z. Peng}, Acta Math. Appl. Sin. 34, No. 1, 24--32 (2011; Zbl 1240.60135)