On the infinitesimal dispersion of multivariate Markov counting systems
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.
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Volume (Year): 82 (2012)
Issue (Month): 4 ()
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- 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.
- Carles Bretó & Edward L. Ionides, 2011. "Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems," Statistics and Econometrics Working Papers ws111914, Universidad Carlos III, Departamento de Estadística y Econometría.
- Kumar, A. & Nane, Erkan & Vellaisamy, P., 2011. "Time-changed Poisson processes," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1899-1910.
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