Fractional poisson processes and related planar random motions

Electronic Journal of Probability

Volumn 14, Issue , 2009, Pages 1790-1826

  Beghin, L ^a   Orsingher, E ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Compound Poisson process; Cylindrical waves; Finite velocity random motions; Fractional derivative; Fractional heat wave equations; Mittag Leffler function; Order statistics; Random velocity motions

Indexed keywords

EID: 70349472846     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v14-675     Document Type: Article

References (14)

1. Jumarie G. (2001), Fractional master equation: non-standard analysis and Liouville-Riemann derivative, Chaos, Solitons and Fractals, 12, 2577-2587
2. Kolesnik A., Orsingher, E. (2005), A planar random motion with an infinite number of directions controlled by the damped wave equation, Journ. Appl. Prob., 42, (4), 1168-1182
3. Laskin, N. (2003), Fractional Poisson process, Communications in Nonlinear Science and Numerical Simulation, 8, 201-213
4. Orsingher, E. (1985), Vibrations with random initial conditions, Bollettino dell’Unione Matematica Italiana, 6, 4-B, 541-556
5. Orsingher, E., Beghin, L. (2004), Time-fractional equations and telegraph processes with Brownian time, Probability Theory and Related Fields, 128, 141-160
6. Orsingher, E., Beghin, L. (2009), Fractional diffusion equations and processes with randomly-varying time, Annals of Probability, 37 (1), 206-249
7. Orsingher, E., De Gregorio A. (2007), Random flights in higher spaces, Journ. Theor. Prob., 20, n.4, 769-806
8. Podlubny, I. (1999), Fractional Differential Equations, Academic Press, San Diego
9. Repin O.N., Saichev, A.I. (2000), Fractional Poisson law, Radiophysics and Quantum Electronics, 43 (9), 738-741
10. Samko, S.G., Kilbas, A.A., Marichev, O.I. (1993), Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers
11. Smirnov VI. (1981), Corso di Matematica Superiore, vol.II, Ed. Riuniti.
12. Stadje, W., Zacks, S. (2004), Telegraph processes with random velocities, Journ. Appl. Prob., 3, 665-678
13. Wang, X.T., Wen, Z.X., Zhang, S.Y. (2006), Fractional Poisson process (II), Chaos, Solitons and Fractals, 28, 143-147
14. Wang, X.T., Zhang, S.Y., Fan S. (2007), Non-homogeneous fractional Poisson processes, Chaos, Solitons and Fractals, 31, 236-241