Alternative numerical computation of one-sided Lévy and Mittag-Leffler distributions

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 2, 2011, Pages

  Saa, Alberto ^a   Venegeroles, Roberto ^b  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b UNIVERSIDADE FEDERAL DO ABC   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

DISTRIBUTION FUNCTIONS; PROBABILITY DISTRIBUTIONS; RATIONAL FUNCTIONS;

CLOSED-FORM FORMULAE; CUMULATIVE DISTRIBUTION FUNCTION; DYNAMICAL BEHAVIORS; INTEGRAL REPRESENTATION; INTERMITTENT SYSTEMS; MEIJER G FUNCTIONS; NUMERICAL COMPUTATIONS; STABLE DISTRIBUTIONS;

PROBABILITY DENSITY FUNCTION;

EID: 80051653323     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.026702     Document Type: Article

References (22)

1. S. Albeverio, G. Casati, and D. Merlini, eds., Stochastic Processes in Classical and Quantum Systems, Lecture Notes in Physics 262 (Springer, Berlin, 1986);
2. M. F. Shlesinger, G. M. Zaslavsky, and U. Frisch, eds., Lévy Flights and Related Topics in Physics, Lecture Notes in Physics 450 (Springer, Berlin, 1995).
3. O. E. Barndorff-Nielsen, T. Mikosch, and S. I. Resnick, eds., Levy Processes: Theory and Applications (Birkhäuser, Boston, 2001);
4. F. Bardou, J.-P. Bouchaud, A. Aspect, and C. Cohen-Tannoudji, Lévy Statistics and Laser Cooling (Cambridge University Press, Cambridge, England, 2002).
5. K. A. Penson and K. Górska, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.210604 105, 210604 (2010).
6. E. Barkai, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.63.046118 63, 046118 (2001).
7. [http://library.wolfram.com/infocenter/MathSource/4377/].
8. [http://math.bu.edu/people/mveillet/html/alphastablepub.html]
9. Namely, formula 2.2.1.19 in A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 5 (Gordon and Breach, Amsterdam, 1998).
10. F. W. J. Olver, NIST Handbook of Mathematical Functions (Cambridge University Press, New York, 2010).
11. W. Feller, An Introduction to Probability Theory and Its Applications Vol. II (Wiley, New York, 1971).
12. J. Mikusinski, Stud. Math. 18, 191 (1959).
13. B. J. West, P. Grigolini, R. Metzler, and T. F. Nonnenmacher, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.55.99 55, 99 (1997).
14. F. Mainardi, P. Paradisi, and R. Gorenflo, preprint arXiv: 0704.0320.
15. J. P. Nolan, Commun. Statist.-Stochastic Models PRLTAO 1532-6349 10.1080/15326349708807450 13, 759 (1997).
16. [http://academic2.american.edu/~jpnolan/stable/stable.html].
17. [http://www.netlib.org/slatec/guide].
18. [http://vigo.ime.unicamp.br/distr].
19. N. Korabel and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.050601 102, 050601 (2009);
20. N. Korabel and E. Barkai, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.016209 82, 016209 (2010).
21. J. Aaronson, An Introduction to Infinite Ergodic Theory (American Mathematical Society, Providence, RI, 1997).
22. T. Akimoto and Y. Aizawa, J. Korean Phys. Soc. KPSJAS 0374-4884 10.3938/jkps.50.254 50, 254 (2007).