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

Edward L. Ionides and Carles Bretó

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

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 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)
Date: 2011-07
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