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The supremum of a Gaussian process over a random interval

Author

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  • Debicki, Krzystof
  • Zwart, Bert
  • Borst, Sem

Abstract

The aim of this note is to give the exact asymptotics ofwhere {X(t): t[greater-or-equal, slanted]0} is a centered Gaussian process with stationary increments and T is an independent non-negative random variable with regularly varying tail distribution. In addition, we obtain explicit lower and upper bounds for the prefactor. As an example we analyze the case of X(t) being a fractional Brownian motion and a Gaussian integrated process.

Suggested Citation

  • Debicki, Krzystof & Zwart, Bert & Borst, Sem, 2004. "The supremum of a Gaussian process over a random interval," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 221-234, July.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:3:p:221-234
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    References listed on IDEAS

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    1. Asmussen, Søren & Klüppelberg, Claudia & Sigman, Karl, 1999. "Sampling at subexponential times, with queueing applications," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 265-286, February.
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    Cited by:

    1. Tan, Zhongquan & Hashorva, Enkelejd, 2013. "Exact asymptotics and limit theorems for supremum of stationary χ-processes over a random interval," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2983-2998.
    2. Arendarczyk, Marek & Dȩbicki, Krzysztof, 2012. "Exact asymptotics of supremum of a stationary Gaussian process over a random interval," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 645-652.

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