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	10.1239/jap/1134587814
Journal	Journal of applied probability
Issue Number	4
Volume Number	42
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2005-12-01
Access Restriction	Open
Subject Keyword	Journal of applied probability Markov Renewal Process
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty