The distribution of apparent occupancy times in a two-state Markov process in which brief events cannot be detected
- 1 June 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 24 (02), 288-301
- https://doi.org/10.1017/s0001867800047534
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
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