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arXiv · 1003.0173

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

Carles Breto·Edward L. Ionides
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Abstract

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 Levy-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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Carles Breto, Edward L. Ionides. 2010-02-28. Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems. https://doi.org/10.1016/j.spa.2011.07.005

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