Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems
| Autor: | Carles Bretó, Edward L. Ionides |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Statistics and Probability
Markov process Mathematics - Statistics Theory Statistics Theory (math.ST) 01 natural sciences Time reversibility 010104 statistics & probability 03 medical and health sciences symbols.namesake Markov renewal process Simple (abstract algebra) Modelling and Simulation Infinitesimal over-dispersion FOS: Mathematics Statistical physics 0101 mathematics Simultaneous events Birth-death process 030304 developmental biology Mathematics Discrete mathematics 0303 health sciences Markov chain Applied Mathematics Birth–death process White noise Counting Markov process Moment (mathematics) Continuous time Modeling and Simulation symbols Environmental stochasticity |
| Zdroj: | Stochastic Processes and their Applications. 121:2571-2591 |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2011.07.005 |
| Popis: | 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. 26 pages |
| Databáze: | OpenAIRE |
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