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Trajectory composition of Poisson time changes and Markov counting systems

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  • Bretó, Carles

Abstract

Changing time of simple continuous-time Markov counting processes by independent unit-rate Poisson processes results in Markov counting processes for which we provide closed-form transition rates via composition of trajectories and with which we construct novel, simpler infinitesimally over-dispersed processes.

Suggested Citation

  • Bretó, Carles, 2014. "Trajectory composition of Poisson time changes and Markov counting systems," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 91-98.
    • Handle: RePEc:eee:stapro:v:88:y:2014:i:c:p:91-98
    DOI: 10.1016/j.spl.2014.01.032
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. 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.
    3. 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.
    4. Nicolai, R.P. & Frenk, J.B.G. & Dekker, R., 2007. "Modelling and optimizing imperfect maintenance of coatings on steel structures," Econometric Institute Research Papers EI 2007-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Kumar, A. & Nane, Erkan & Vellaisamy, P., 2011. "Time-changed Poisson processes," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1899-1910.
    6. Sourya Shrestha & Aaron A King & Pejman Rohani, 2011. "Statistical Inference for Multi-Pathogen Systems," PLOS Computational Biology, Public Library of Science, vol. 7(8), pages 1-14, August.
    7. Bretó, Carles, 2012. "On the infinitesimal dispersion of multivariate Markov counting systems," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 720-725.
    8. Jim Jackson, 2002. "How Networks of Queues Came About," Operations Research, INFORMS, vol. 50(1), pages 112-113, February.
    9. 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.
    10. Varughese, M.M. & Fatti, L.P., 2008. "Incorporating environmental stochasticity within a biological population model," Theoretical Population Biology, Elsevier, vol. 74(1), pages 115-129.
    11. 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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