Time spent below a random threshold by a Poisson driven sequence of observations
Exceedance statistics, Limit theorems, Nonhomogeneous Poisson process, Order statistics, Poisson driven sequence of observations, Random threshold
Journal of Applied Probability
The mean and the variance of the time S(t) spent by a system below a random threshold until t are obtained when the system level is modelled by the current value of a sequence of independent and identically distributed random variables appearing at the epochs of a nonhomogeneous Poisson process. In the case of the homogeneous Poisson process, the asymptotic distribution of S(t)/t as t → ∞ is derived.
Original Publication Date
DOI of published version
Kirmani, S. N.U.A. and Wesołowski, Jacek, "Time spent below a random threshold by a Poisson driven sequence of observations" (2003). Faculty Publications. 3240.