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Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems

  • Bretó, Carles
  • Ionides, Edward L.
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    We propose an infinitesimal dispersion index for Markov counting processes. We show that, under standard moment existence conditions, a process is infinitesimally (over-)equi-dispersed if, and only if, it is simple (compound), i.e. it increases in jumps of one (or more) unit(s), even though infinitesimally equi-dispersed processes might be under-, equi- or over-dispersed using previously studied indices. Compound processes arise, for example, when introducing continuous-time white noise to the rates of simple processes resulting in Lévy-driven SDEs. We construct multivariate infinitesimally over-dispersed compartment models and queuing networks, suitable for applications where moment constraints inherent to simple processes do not hold.

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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 121 (2011)
    Issue (Month): 11 (November)
    Pages: 2571-2591

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    Handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2571-2591
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    1. Fan, Ruzong & Lange, Kenneth & Peña, Edsel, 1999. "Applications of a formula for the variance function of a stochastic process," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 123-130, June.
    2. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342.
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