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Point processes generated by transitions of Markov chains

Published online by Cambridge University Press:  01 July 2016

Mats Rudemo
Mats Rudemo*
Affiliation:
Research Institute of National Defence, Stockholm
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Abstract

For a continuous time Markov chain the time points of transitions, belonging to a subset of the set of all transitions, are observed. Special cases include the point process generated by all transitions and doubly stochastic Poisson processes with a Markovian intensity. Equations are derived for the conditional distribution of the state of the Markov chain, given observations of the point process. This distribution may be used for prediction. For the forward recurrence time of the point process, distributions corresponding to synchronous and asynchronous sampling are also derived. The Palm distribution for the point process is specified in terms of the corresponding initial distribution for the Markov chain. In examples the point processes of arrivals and departures in a queueing system are studied. Two biological applications deal with estimation of population size and detection of epidemics.

Keywords

POINT PROCESSMARKOV CHAINSTATE ESTIMATIONPREDICTION OF POINT PROCESSESPALM PROBABILITIESDOUBLY STOCHASTIC POISSON PROCESSESESTIMATION OF POPULATION SIZEDETECTION OF EPIDEMICS
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 2 , August 1973 , pp. 262 - 286
Copyright
Copyright © Applied Probability Trust 1973 

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