Simulation and Estimation for the Fractional Yule Process

Methodology and Computing in Applied Probability

Volumn 14, Issue 2, 2012, Pages 383-403

  Cahoy, Dexter O ^a   Polito, Federico ^b  

^a Louisiana Tech University   (United States)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Birth process; Fractional calculus; Mittag Leffler; Poisson process; Wright; Yule Furry process

Indexed keywords

EID: 84859783908     PISSN: 13875841     EISSN: 15737713     Source Type: Journal    
DOI: 10.1007/s11009-010-9207-6     Document Type: Article

References (24)

1. Beghin L, Orsingher E (2009) Fractional poisson processes and related planar random motions. Electron J Probab 14(61): 1790-1827.
2. Cahoy DO (2007) Fractional poisson process in terms of alpha-stable densities. USA.
3. Cahoy DO, Uchaikin VV, Woyczynski WA (2010) Parameter estimation for fractional poisson processes. J Stat Plan Inference 140(11): 3106-3120.
4. Gradshteyn IS, Ryzhik IM (1980) Table of integrals, series, and products. Academic Press, New York.
5. Harris T (2002) The theory of branching processes. Dover Phoenix, Toronto.
6. Jumarie G (2001) Fractional master equation: non-standard analysis and liouville-riemann derivative. Chaos, Solitons Fractals 12(13): 2577-2587.
7. Keiding N (1974) Estimation in the birth process. Biometrika 61(1): 71-80.
8. Kendall DG (1966) Branching processes since 1873. J Lond Math Soc 41: 385-406.
9. Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier Science.
10. Laskin N (2003) Fractional poisson process. Commun Nonlinear Sci Numer Simul 8(3-4): 201-213.
11. Mainardi F, Gorenflo R, Scalas E (2004) A fractional generalization of poisson processes. Vietnam J Math 32: 53-64.
12. Mainardi F, Gorenflo R, Vivoli A (2005) Renewal processes of mittag-leffler and wright type. Fract Calc Appl Anal 8: 7-38.
13. Mathai AM, Saxena RK, Haubold HJ (2010) The H-function, theory and applications. Springer, New York.
14. McKendrick AG (1914) Studies on the theory of continuous probabilities with special reference to its bearing on natural phenomena of a progressive nature. Proc Lond Math Soc 2(13): 401-416.
15. Orsingher E, Polito F (2010) Fractional pure birth processes. Bernoulli 16(3): 858-881.
16. Paris RB, Kaminski D (2001) Asymptotics and Mellin-Barnes integrals. Cambridge University Press.
17. Podlubny I (1999) Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, some methods of their solution and some of their applications. Academic Press, San Diego.
18. Repin ON, Saichev AI (2000) Fractional poisson law. Radiophys Quantum Electron 43(9): 738-741.
19. Uchaikin VV, Sibatov RT (2008) A fractional poisson process in a model of dispersive charge transport in semiconductors. Russ J Numer Anal Math Model 23(3): 283-297.
20. Uchaikin VV, Cahoy DO, Sibatov RT (2008) Fractional processes: from poisson to branching one. Int J Bifurc Chaos 18(9): 2717-2725.
21. Wang XT, Wen Z-X (2003) Poisson fractional processes. Chaos, Solitons Fractals 18(1): 169-177.
22. Wang XT, Wen Z-X, Zhang S-Y, (2006) Fractional poisson process (ii). Chaos, Solitons Fractals 28(1): 143-147 (2006).
23. Wang XT, Zhang S-Y, Fan S (2007) Nonhomogeneous fractional poisson processes. Chaos, Solitons Fractals 31(1): 236-241 (2007).
24. Waugh WAO (1970) Transformation of a birth process into a poisson process. J R Stat Soc Ser B 32(3): 418-431.