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Joint limit distributions of exceedances point processes and partial sums of gaussian vector sequence

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Abstract

In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence (centered at the sample mean) converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P. R. China

    Zuo Xiang Peng & Jin Jun Tong

  2. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015, Lausanne, Switzerland

    Zhi Chao Weng

Authors
  1. Zuo Xiang Peng
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  2. Jin Jun Tong
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  3. Zhi Chao Weng
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Corresponding author

Correspondence to Zuo Xiang Peng.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 11171275) and the Program for Excellent Talents in Chongqing Higher Education Institutions (Grant No. 120060-20600204); the third author is supported by the Swiss National Science Foundation Project (Grant No. 200021-134785)

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Peng, Z.X., Tong, J.J. & Weng, Z.C. Joint limit distributions of exceedances point processes and partial sums of gaussian vector sequence. Acta. Math. Sin.-English Ser. 28, 1647–1662 (2012). https://doi.org/10.1007/s10114-012-0001-y

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  • DOI: https://doi.org/10.1007/s10114-012-0001-y

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