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Joint asymptotic distribution of exceedances point processes and partial sums of strong dependent non-stationary Gaussian sequences. (Chinese. English summary) Zbl 1240.60135

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.

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G70 Extreme value theory; extremal stochastic processes
60G15 Gaussian processes
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