Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems
Edward L. Ionides and
DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística
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 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.
Keywords: Continuous; time; Counting; Markov; process; Birth-death; process; Environmental; stochasticity; Infinitesimal; over-dispersion; Simultaneous; events (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:ws111914
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