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Limit results for maxima in non-stationary multivariate Gaussian sequences

Author

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  • Hüsler, Jürg
  • Schüpbach, Michel

Abstract

Let {Xk, k[greater-or-equal, slanted]1} be a multivariate Gaussian sequence, and Mn be the partial maxima, taken componentwise, i.e. Mni=max{Xki,k[less-than-or-equals, slant]n}, for any i [less-than-or-equals, slant] p. We deal with the limiting behaviour of the distribution of Mn and show that, under certain conditions, this limit distribution is equal to the product of the marginal limit distributions of the Mni's or to the asymptotic product of the distributions of the Xk's.

Suggested Citation

  • Hüsler, Jürg & Schüpbach, Michel, 1988. "Limit results for maxima in non-stationary multivariate Gaussian sequences," Stochastic Processes and their Applications, Elsevier, vol. 28(1), pages 91-99, April.
  • Handle: RePEc:eee:spapps:v:28:y:1988:i:1:p:91-99
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    Cited by:

    1. James, Barry & James, Kang & Qi, Yongcheng, 2007. "Limit distribution of the sum and maximum from multivariate Gaussian sequences," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 517-532, March.

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