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.Â 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 InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 121 (2011)
Issue (Month): 11 (November)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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