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On the infinitesimal dispersion of multivariate Markov counting systems

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  • Bretó, Carles

Abstract

We provide a multivariate extension of a recent result for univariate Markov counting processes: necessity and sufficiency of compoundness for infinitesimal over-dispersion. As an illustration, we show that infinitesimally over-dispersed epidemiological SIR-type compartment models must rely on compound counting processes.

Suggested Citation

  • Bretó, Carles, 2012. "On the infinitesimal dispersion of multivariate Markov counting systems," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 720-725.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:720-725
    DOI: 10.1016/j.spl.2011.12.019
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    References listed on IDEAS

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    1. Bretó, Carles & Ionides, Edward L., 2011. "Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems," DES - Working Papers. Statistics and Econometrics. WS ws111914, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Kumar, A. & Nane, Erkan & Vellaisamy, P., 2011. "Time-changed Poisson processes," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1899-1910.
    3. Bretó, Carles & Ionides, Edward L., 2011. "Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2571-2591, November.
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    Cited by:

    1. Bretó, Carles, 2014. "Trajectory composition of Poisson time changes and Markov counting systems," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 91-98.

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