Article ID Journal Published Year Pages File Type
1155819 Stochastic Processes and their Applications 2011 21 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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