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Central limit theorems for multivariate semi-Markov sequences and processes, with applications

Part of: Special processes Physiological, cellular and medical topics Limit theorems

Published online by Cambridge University Press:  14 July 2016

Frank Ball
Frank Ball*
Affiliation:
University of Nottingham
*
∗Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK. Email address: [email protected]
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Abstract

In this paper, central limit theorems for multivariate semi-Markov sequences and processes are obtained, both as the number of jumps of the associated Markov chain tends to infinity and, if appropriate, as the time for which the process has been running tends to infinity. The theorems are widely applicable since many functions defined on Markov or semi-Markov processes can be analysed by exploiting appropriate embedded multivariate semi-Markov sequences. An application to a problem in ion channel modelling is described in detail. Other applications, including to multivariate stationary reward processes, counting processes associated with Markov renewal processes, the interpretation of Markov chain Monte Carlo runs and statistical inference on semi-Markov models are briefly outlined.

Keywords

Aggregated processmultivariate central limit theoremmultivariate semi-Markov processmultivariate semi-Markov sequencereward processsingle ion channel modellingstationary processtime interval omission

MSC classification

Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60F05: Central limit and other weak theorems 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 92C05: Biophysics
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 415 - 432
Copyright
Copyright © Applied Probability Trust 1999 

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