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On aggregated Markov processes

Published online by Cambridge University Press:  14 July 2016

Donald R. Fredkin*
Affiliation:
University of California, San Diego
John A. Rice*
Affiliation:
University of California, San Diego
*
Postal address: Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA.
∗∗Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA.

Abstract

A finite-state Markov process is aggregated into several groups. What can be learned about the underlying process from the aggregated one? We provide some partial answers to this question.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1986 

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References

Colquhoun, D. and Hawkes, A. G. (1981) On the stochastic properties of single ion channels. Proc. R. Soc. London B 211, 205235.Google Scholar
Colquhoun, 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. London B 300, 159.Google Scholar
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.Google Scholar
Fredkin, D. R., Montal, M. and Rice, J. (1983) Identification of aggregated Markovian models: application to the nicotinic acetylcholine receptor. Proc. Berkeley Conf. Honor of Jerzy Neyman and Jack Kiefer 1, ed. Le Cam, L. and Olshen, R., Wadsworth, Belmont, CA, 269290.Google Scholar
Horn, R. and Lange, K. (1983) Estimating kinetic constants from single channel data. Biophys. J 43, 207223.Google Scholar
Kemeny, J. G. and Snell, L. J. (1960) Finite Markov Chains. Van Nostrand, Princeton NJ.Google Scholar
Labarca, P., Rice, J., Fredkin, D. R. and Montal, M. (1984) Kinetic analysis of channel gating: application to the cholinergic receptor channel and the chloride channel from Torpedo californica . Biophys. J. 47, 469478.CrossRefGoogle Scholar