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On extremes and streams of upcrossings

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  • Albin, J. M. P.

Abstract

We study relations between P{supt[set membership, variant][0,h] [xi](t)>u} and for a stationary process [xi](t). Applications include Markov jump processes, [alpha]-stable processes, and quadratic functionals of Gaussian processes.

Suggested Citation

  • Albin, J. M. P., 2001. "On extremes and streams of upcrossings," Stochastic Processes and their Applications, Elsevier, vol. 94(2), pages 271-300, August.
    • Handle: RePEc:eee:spapps:v:94:y:2001:i:2:p:271-300
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    References listed on IDEAS

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    1. Samorodnitsky, Gennady, 1988. "Extrema of skewed stable processes," Stochastic Processes and their Applications, Elsevier, vol. 30(1), pages 17-39, November.
    2. Albin, J. M. P., 1992. "Extremes and crossings for differentiable stationary processes with application to Gaussian processes in m and Hilbert space," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 119-147, August.
    3. Albin, J. M. P., 2000. "Extremes and upcrossing intensities for P-differentiable stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 199-234, June.
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    Cited by:

    1. Aue, Alexander & Horvth, Lajos & Huskov, Marie, 2009. "Extreme value theory for stochastic integrals of Legendre polynomials," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1029-1043, May.

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    1. Albin, J. M. P., 2000. "Extremes and upcrossing intensities for P-differentiable stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 199-234, June.
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