Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T13:59:44.920Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Integral transforms, operational calculus Physiological, cellular and medical topics Markov 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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ball, F. G. and Sansom, M. S. P. (1988) Aggregated Markov processes incorporating time interval omission. Adv. Appl. Prob. 20, 546–572.CrossRefGoogle Scholar
Ball, F. G. and Sansom, M. S. P. (1989) Ion channel gating mechanisms: model identification and parameter estimation from single channel recordings. Proc. R. Soc. Lond. B 236, 385–416.Google Scholar
Blatz, A. L. and Magleby, K. L. (1986) Correcting single channel data for missed events. Biophys. J. 49, 967–980.Google Scholar
Boas, R. P. (1954) Entire Functions. Academic Press, New York.Google Scholar
Colouhoun, D. and Hawkes, A. G. (1982) On the stochastic properties of bursts of single ion channel openings and of clusters of bursts. Phil. Trans. R. Soc. Lond. B 300, 1–59.Google Scholar
Colquhoun, D. and Sigworth, F. J. (1983) Fitting and statistical analysis of single channel records. In Single Channel Recording, ed. Sakmann, B. and Neher, E., Plenum, New York, 191–263.CrossRefGoogle Scholar
Crouzy, S. C. and Sigworth, F. J. (1990) Yet another approach to the dwell time omission problem of single channel analysis. Biophys. J. 58, 731–743.CrossRefGoogle Scholar
Hawkes, A. G. and Jalali, A. (1991) Asymptotic distributions of apparent open times and shut times in a single channel record allowing for the omission of brief events. University of Wales, Swansea, Working Paper EMBS/1991/3.Google Scholar
Hawkes, A. G., Jalali, A. and Colquhoun, D. (1990) The distributions of the apparent open times and shut times in a single channel record when brief events can not be detected. Phil. Trans R. Soc. Lond. A 332, 511–538.Google Scholar
Hawkes, A. G., Jalali, A. and Colquhoun, D. (1992) Asymptotic distributions of apparent open times and shut times in a single channel record allowing for the omission of brief events. Phil. Trans. R. Soc. London. To appear.Google Scholar
Jalali, A. and Hawkes, A. G. (1992) Generalised eigenproblems arising in aggregated Markov processes allowing for time interval omission. Adv. Appl. Prob. 24, 302–321.Google Scholar
Markushevich, A. I. (1965) Theory of Functions of a Complex Variable. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Roux, B. and Sauve, R. (1985) A general solution of the time interval omission problem applied to single channel analysis. Biophys. J. 48, 149–158.Google Scholar
Smith, M. G. (1966) Laplace Transofrm Theory. Van Nostrand, London.Google Scholar
Yeo, G. F., Milne, R. K., Edeson, R. O. and Madsen, B. W. (1988) Statistical inference from single channel records: two-state Markov model with limited time resolution. Proc. R. Soc. Lond. B 235, 63–94.Google Scholar