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Generalised eigenproblems arising in aggregated markov processes allowing for time interval omission

Part of: Markov processes Basic linear algebra Physiological, cellular and medical topics Special processes

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 continuous-time Markov chain in which one cannot observe individual states but only which of two sets of states is occupied at any time. Furthermore, we suppose that the resolution of the recording apparatus is such that small sojourns, of duration less than a constant deadtime, cannot be observed. We obtain some results concerning the poles of the Laplace transform of the probability density function of apparent occupancy times, which correspond to a problem about generalised eigenvalues and eigenvectors. These results provide useful asymptotic approximations to the probability density of occupancy times. A numerical example modelling a calcium-activated potassium channel is given. Some generalisations to the case of random deadtimes complete the paper.

Keywords

EIGENVALUESOCCUPANCY TIMESION CHANNELS

MSC classification

Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 15A18: Eigenvalues, singular values, and eigenvectors 92C05: Biophysics 92C30: Physiology (general)
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 2 , June 1992 , pp. 302 - 321
Copyright
Copyright © Applied Probability Trust 1992 

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