Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems
AbstractWe 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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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws111914.
Date of creation: Jul 2011
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Continuous time; Counting Markov process; Birth-death process; Environmental stochasticity; Infinitesimal over-dispersion; Simultaneous events;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-02 (All new papers)
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- Bretó, Carles, 2012. "On the infinitesimal dispersion of multivariate Markov counting systems," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 720-725.
- Bretó, Carles, 2014. "Trajectory composition of Poisson time changes and Markov counting systems," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 91-98.
- Bretó, Carles, 2012. "Time changes that result in multiple points in continuous-time Markov counting processes," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2229-2234.
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