Sojourn Times of Gaussian Processes with Random Parameters

Goran Popivoda () and Siniša Stamatović ()
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Goran Popivoda: University of Montenegro
Siniša Stamatović: University of Montenegro

Journal of Theoretical Probability, 2024, vol. 37, issue 3, 2023-2053

Abstract: 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.

Keywords: Sojourn times; Conditionally Gaussian process; Gaussian process; Stationary random process; 60G15; 60G60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01305-1

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