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Time changes that result in multiple points in continuous-time Markov counting processes

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  • Bretó, Carles

Abstract

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.

Suggested Citation

  • Bretó, Carles, 2012. "Time changes that result in multiple points in continuous-time Markov counting processes," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2229-2234.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2229-2234 DOI: 10.1016/j.spl.2012.08.006
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    References listed on IDEAS

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    1. Bretó, Carles & Ionides, Edward L., 2011. "Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems," DES - Working Papers. Statistics and Econometrics. WS ws111914, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Kumar, A. & Nane, Erkan & Vellaisamy, P., 2011. "Time-changed Poisson processes," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1899-1910.
    3. Hélyette Geman & Dilip B. Madan & Marc Yor, 2001. "Time Changes for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 79-96.
    4. 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.
    5. 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.
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    Cited by:

    1. Bretó, Carles, 2014. "Trajectory composition of Poisson time changes and Markov counting systems," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 91-98.

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