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Asymptotic distribution of sum and maximum for Gaussian processes

  • Hwai-Chung Ho (a1) and William P. McCormick (a2)

Let {X n , n ≥ 0} be a stationary Gaussian sequence of standard normal random variables with covariance function r(n) = E X 0 X n . Let Under some mild regularity conditions on r(n) and the condition that r(n)lnn = o(1) or (r(n)lnn)−1 = O(1), the asymptotic distribution of is obtained. Continuous-time results are also presented as well as a tube formula tail area approximation to the joint distribution of the sum and maximum.

Corresponding author
Postal address: Institute of Statistical Science, Academia Sinica, Taipei, Taiwan, ROC.
∗∗ Postal address: Department of Statistics, University of Georgia, Athens, GA 30602, USA. Email address:
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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