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Sojourn Times of Gaussian Processes with Random Parameters

Author

Listed:
  • Goran Popivoda

    (University of Montenegro)

  • Siniša Stamatović

    (University of Montenegro)

Abstract

In this paper, we investigate the sojourn times of conditionally Gaussian processes, i.e., the sojourns of $$\xi (t)+\lambda -\zeta \,t^\beta $$ ξ ( t ) + λ - ζ t β and $$\xi (t)(\lambda -\zeta \,t^\beta )$$ ξ ( t ) ( λ - ζ t β ) , $$t\in [0, T],\ T>0$$ t ∈ [ 0 , T ] , T > 0 , where $$\xi $$ ξ is a Gaussian zero-mean stationary process and $$\lambda $$ λ and $$\zeta $$ ζ are random variables independent of $$\xi (\cdot )$$ ξ ( · ) , and $$\beta >0$$ β > 0 is a constant.

Suggested Citation

  • Goran Popivoda & Siniša Stamatović, 2024. "Sojourn Times of Gaussian Processes with Random Parameters," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2023-2053, September.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:3:d:10.1007_s10959-023-01305-1
    DOI: 10.1007/s10959-023-01305-1
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    References listed on IDEAS

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    1. Krzysztof Dȩbicki & Zbigniew Michna & Xiaofan Peng, 2019. "Approximation of Sojourn Times of Gaussian Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1183-1213, December.
    2. Enkelejd Hashorva & Anthony G. Pakes & Qihe Tang, 2010. "Asymptotics of Random Contractions," Papers 1008.0126, arXiv.org.
    3. Hösler, Jörg & Piterbarg, Vladimir & Rumyantseva, Ekaterina, 2011. "Extremes of Gaussian processes with a smooth random variance," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2592-2605, November.
    4. Popivoda, Goran & Stamatović, Siniša, 2019. "On probability of high extremes of Gaussian fields with a smooth random trend," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 29-35.
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