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Aggregated Markov processes incorporating time interval omission

Published online by Cambridge University Press:  01 July 2016

Frank Ball  and
Mark Sansom
Frank Ball*
Affiliation:
University of Nottingham
Mark Sansom*
Affiliation:
University of Nottingham
*
∗Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
∗∗Postal address: Department of Zoology, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
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Abstract

We consider a finite-state-space, continuous-time Markov chain which is time reversible. The state space is partitioned into two sets, termed ‘open' and ‘closed', and it is only possible to observe which set the process is in. Further, short sojourns in either the open or closed sets of states will fail to be detected. We show that the dynamic stochastic properties of the observed process are completely described by an embedded Markov renewal process. The parameters of this Markov renewal process are obtained, allowing us to derive expressions for the moments and autocorrelation functions of successive sojourns in both the open and closed states. We illustrate the theory with a numerical study.

Keywords

TIME REVERSIBLE PROCESSMARKOV RENEWAL PROCESSEMBEDDED PROCESSSINGLE CHANNEL GATING KINETICS
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 3 , September 1988 , pp. 546 - 572
Copyright
Copyright © Applied Probability Trust 1988 

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