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Abstract and Applied Analysis
Volume 2012, Article ID 747503, 30 pages
http://dx.doi.org/10.1155/2012/747503
Research Article

Alternative Forms of Compound Fractional Poisson Processes

1Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
2Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy

Received 11 May 2012; Revised 26 August 2012; Accepted 9 September 2012

Academic Editor: Bashir Ahmad

Copyright © 2012 Luisa Beghin and Claudio Macci. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [10 citations]

The following is the list of published articles that have cited the current article.

  • Mohsen Alipour, Luisa Beghin, and Davood Rostamy, “Generalized Fractional Nonlinear Birth Processes,” Methodology and Computing in Applied Probability, 2013. View at Publisher · View at Google Scholar
  • Mirko DʼOvidio, “Continuous random walks and fractional powers of operators,” Journal of Mathematical Analysis and Applications, 2013. View at Publisher · View at Google Scholar
  • Živorad Tomovski, Tibor K. Pogány, and H.M. Srivastava, “Laplace type integral expressions for a certain three-parameter family of generalized mittag-leffler functions with applications involving complete monotonicity,” Journal of the Franklin Institute, 2014. View at Publisher · View at Google Scholar
  • Luisa Beghin, “On fractional tempered stable processes and their governing differential equations,” Journal of Computational Physics, 2014. View at Publisher · View at Google Scholar
  • Ying Wang, Dehui Wang, and Fukang Zhu, “Estimation of Parameters in the Fractional Compound Poisson Process,” Communications in Nonlinear Science and Numerical Simulation, 2014. View at Publisher · View at Google Scholar
  • Luisa Beghin, and Claudio Macci, “Fractional discrete processes: Compound and mixed poisson representations,” Journal of Applied Probability, vol. 51, no. 1, pp. 19–36, 2014. View at Publisher · View at Google Scholar
  • Luisa Beghin, “Fractional Gamma and Gamma-Subordinated Processes,” Stochastic Analysis and Applications, vol. 33, no. 5, pp. 903–926, 2015. View at Publisher · View at Google Scholar
  • Dumitru Baleanu, and Mohsen Alipour, “On the kolmogorov forward equations within Caputo and Riemann-Liouville fractions derivatives,” Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, vol. 24, no. 3, pp. 5–20, 2016. View at Publisher · View at Google Scholar
  • Federico Polito, and Enrico Scalas, “A generalization of the space-fractional Poisson process and its connection to some Lévy processes,” Electronic Communications in Probability, vol. 21, 2016. View at Publisher · View at Google Scholar
  • Kobylych, and Sakhno, “Point processes subordinated to compound poisson processes,” Theory of Probability and Mathematical Statistics, vol. 94, pp. 89–96, 2017. View at Publisher · View at Google Scholar