Time Spent Below A Random Threshold By A Poisson Driven Sequence Of Observations

Authors

S. N.U.A. Kirmani, University of Northern IowaFollow
Jacek Wesołowski, Politechnika Warszawska

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.

Department

Department of Mathematics

Original Publication Date

9-1-2003

DOI of published version

10.1239/jap/1059060907

Recommended Citation

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.
https://scholarworks.uni.edu/facpub/3240