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Asymptotic crossing rates for stationary Gaussian vector processes

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  • Breitung, Karl

Abstract

For stationary differentiable Gaussian vector processes the expected number of crossings through a hypersurface is given by a surface integral. In general, this is difficult to calculate. In this paper asymptotic approximations for these surface integrals are derived.

Suggested Citation

  • Breitung, Karl, 1988. "Asymptotic crossing rates for stationary Gaussian vector processes," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 195-207, September.
    • Handle: RePEc:eee:spapps:v:29:y:1988:i:2:p:195-207
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    Cited by:

    1. Wang, Zequn & Chen, Wei, 2016. "Time-variant reliability assessment through equivalent stochastic process transformation," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 166-175.
    2. Jian Wang & Xiang Gao & Zhili Sun, 2021. "A Multilevel Simulation Method for Time-Variant Reliability Analysis," Sustainability, MDPI, vol. 13(7), pages 1-16, March.
    3. Li, Junxiang & Chen, Jianqiao, 2019. "Solving time-variant reliability-based design optimization by PSO-t-IRS: A methodology incorporating a particle swarm optimization algorithm and an enhanced instantaneous response surface," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    4. Jian Wang & Xiang Gao & Zhili Sun, 2021. "An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes," Sustainability, MDPI, vol. 13(14), pages 1-16, July.
    5. Xu, Sheng & Wang, Shan & Guedes Soares, C., 2019. "Review of mooring design for floating wave energy converters," Renewable and Sustainable Energy Reviews, Elsevier, vol. 111(C), pages 595-621.
    6. Wang, Zequn & Wang, Pingfeng, 2013. "A new approach for reliability analysis with time-variant performance characteristics," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 70-81.
    7. Zhang, Yang & Xu, Jun & Gardoni, Paolo, 2024. "A loading contribution degree analysis-based strategy for time-variant reliability analysis of structures under multiple loading stochastic processes," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    8. Hawchar, Lara & El Soueidy, Charbel-Pierre & Schoefs, Franck, 2017. "Principal component analysis and polynomial chaos expansion for time-variant reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 406-416.
    9. Zhang, Yang & Xu, Jun & Beer, Michael, 2023. "A single-loop time-variant reliability evaluation via a decoupling strategy and probability distribution reconstruction," Reliability Engineering and System Safety, Elsevier, vol. 232(C).

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