Simple Derivations of Properties of counting processes associated with Markov Renewal Processes

F. Ball, Robin Milne

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)

    Abstract

    A simple, widely applicable method is described for determining factorial moments of (N) over cap (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 -> infinity. The factorial moment formulae combine to yield an expression for the probability generating function of (N) over cap (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.
    Original languageEnglish
    Pages (from-to)1031-1043
    JournalJournal of Applied Probability
    Volume42
    Issue number4
    DOIs
    Publication statusPublished - 2005

    Fingerprint

    Dive into the research topics of 'Simple Derivations of Properties of counting processes associated with Markov Renewal Processes'. Together they form a unique fingerprint.

    Cite this