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Extremes, rainflow cycles and damage functionals in continuous random processes

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  • Rychlik, Igor

Abstract

We discuss some properties of damage functionals defined on a sequence of local extremes in continuous stochastic processes both irregular, e.g. Brownian motion, diffusions, and smooth, e.g. stationary Gaussian processes with finite intensity of local maxima. Local extremes are represented as a point process in R2. The main tools are rainflow cycles and oscillation measures.

Suggested Citation

  • Rychlik, Igor, 1996. "Extremes, rainflow cycles and damage functionals in continuous random processes," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 97-116, October.
    • Handle: RePEc:eee:spapps:v:63:y:1996:i:1:p:97-116
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    References listed on IDEAS

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    1. Scheutzow, Michael, 1994. "A law of large numbers for upcrossing measures," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 285-305, October.
    2. Rychlik, Igor, 1987. "A note on Durbin's formula for the first-passage density," Statistics & Probability Letters, Elsevier, vol. 5(6), pages 425-428, October.
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