Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2010
- DOI:
- 10.48550/arXiv.1003.0173
- arXiv:
- arXiv:1003.0173
- Bibcode:
- 2010arXiv1003.0173B
- Keywords:
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- Mathematics - Statistics Theory
- E-Print:
- 26 pages