Faculty Publications

Title

Time spent below a random threshold by a Poisson driven sequence of observations

Document Type

Article

Keywords

Exceedance statistics, Limit theorems, Nonhomogeneous Poisson process, Order statistics, Poisson driven sequence of observations, Random threshold

Journal/Book/Conference Title

Journal of Applied Probability

Volume

40

Issue

3

First Page

807

Last Page

814

Abstract

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

9-1-2003

DOI of published version

10.1239/jap/1059060907

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