Time changes that result in multiple points in continuous-time Markov counting processes
We show that randomly changing time of simple, infinitesimally equi-dispersed, non-linear birth–death processes can result in compound, infinitesimally over-dispersed processes. We provide sufficient and necessary conditions and illustrate this with various time changes and examples from scientific and engineering fields.
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Volume (Year): 82 (2012)
Issue (Month): 12 ()
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- Kumar, A. & Nane, Erkan & Vellaisamy, P., 2011. "Time-changed Poisson processes," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1899-1910.
- Carles Bretó & Edward L. Ionides, 2011. "Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems," Statistics and Econometrics Working Papers ws111914, Universidad Carlos III, Departamento de Estadística y Econometría.
- Hélyette Geman & Dilip B. Madan & Marc Yor, 2001. "Time Changes for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 79-96.
- M. J. Faddy & J. S. Fenlon, 1999. "Stochastic modelling of the invasion process of nematodes in fly larvae," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 31-37.
- Bretó, Carles & Ionides, Edward L., 2011. "Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2571-2591, November.
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