Joint asymptotic distribution of exceedances point process and partial sum of stationary Gaussian sequence

Let { X i } i =1 ∞ be a standardized stationary Gaussian sequence with covariance function r ( n ) = EX 1 X n +1 , S n = Σ i =1 n X i , and . And let N n be the point process formed by the exceedances of random level by X 1 , X 2 ,…, X n . Under some mild conditions, N n and S n are asymptotically i...

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Bibliographic Details
Published in:Applied Mathematics-A Journal of Chinese Universities 2011-09, Vol.26 (3), p.319-326
Main Authors: Tan, Zhong-quan, Peng, Zuo-xiang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:Let { X i } i =1 ∞ be a standardized stationary Gaussian sequence with covariance function r ( n ) = EX 1 X n +1 , S n = Σ i =1 n X i , and . And let N n be the point process formed by the exceedances of random level by X 1 , X 2 ,…, X n . Under some mild conditions, N n and S n are asymptotically independent, and N n converges weakly to a Poisson process on (0,1].
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-011-2113-z