Sojourn Times of Gaussian Processes with Random Parameters

Abstract

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