Simple derivations of properties of counting processes associated with Markov renewal processes

Content Provider	Scilit
Author	Ball, Frank Milne, Robin K.
Copyright Year	2005
Description	A simple, widely applicable method is described for determining factorial moments of N̂ t , the number of occurrences in (0,t] of some event defined in terms of an underlying Markov renewal process, and asymptotic expressions for these moments as t → ∞. The factorial moment formulae combine to yield an expression for the probability generating function of N̂ t , and thereby further properties of such counts. The method is developed by considering counting processes associated with events that are determined by the states at two successive renewals of a Markov renewal process, for which it both simplifies and generalises existing results. More explicit results are given in the case of an underlying continuous-time Markov chain. The method is used to provide novel, probabilistically illuminating solutions to some problems arising in the stochastic modelling of ion channels.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/35FC160D8689838C42F888F2FD0D0E39/S002190020000108Xa.pdf/div-class-title-simple-derivations-of-properties-of-counting-processes-associated-with-markov-renewal-processes-div.pdf
Ending Page	1043
Page Count	13
Starting Page	1031
ISSN	00219002
e-ISSN	14756072
DOI	10.1017/s002190020000108x
Journal	Journal of applied probability
Issue Number	04
Volume Number	42
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2005-12-01
Access Restriction	Open
Subject Keyword	Journal of applied probability Applied Mathematics Mathematical Physics time Markov Chain Counting Process Factorial Moment Factorial Moment Measure Ion Channel Modelling Markov Renewal Process Point Process markov Process Time Interval Omission
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty