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The distribution of apparent occupancy times in a two-state Markov process in which brief events cannot be detected

Part of: Markov processes Physiological, cellular and medical topics Integral transforms, operational calculus

Published online by Cambridge University Press:  01 July 2016

Assad Jalali  and
Alan G. Hawkes
Assad Jalali
Affiliation:
University of Wales, Swansea
Alan G. Hawkes
Affiliation:
University of Wales, Swansea
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Abstract

We consider a two-state Markov process in which the resolution of the recording apparatus is such that small sojourns, of duration less than some constant deadtime τ, cannot be observed: the so-called time interval omission problem. We express the probability density of apparent occupancy times in terms of an exponential and infinitely many damped oscillations. Using a finite number of these gives an extremely accurate approximation to the true density for all except small values of the time t.

Keywords

TIME INTERVAL OMISSIONDAMPED OSCILLATIONS

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 92C05: Biophysics 92C30: Physiology (general) 44A10: Laplace transform
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 2 , June 1992 , pp. 288 - 301
Copyright
Copyright © Applied Probability Trust 1992 

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