Characterizations and simulations of a class of stochastic processes to model anomalous diffusion

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 28, 2008, Pages

  Mura, A ^a   Pagnini, G ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b ENEA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 52349086501     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/28/285003     Document Type: Article

References (37)

1. Ratynskaia S, Rypdal K, Knapek C, Khrapak S, Milovanov A V, Ivlev A, Rasmussen J J and Morfill G E 2006 Phys. Rev. Lett. 96 105010
2. Gambin Y, Massiera G, Ramos L, Ligoure C and Urbach W 2005 Phys. Rev. Lett. 94 110602
3. Labeyrie G, Vaujour E, Müller C A, Delande D, Miniatura C, Wilkowski D and Kaiser R 2003 Phys. Rev. Lett. 91 223904
4. Kou S C and Xie X S 2004 Phys. Rev. Lett. 93 180603
5. Solomon T H, Weeks E R and Swinney H L 1993 Phys. Rev. Lett. 71 3975
6. Marty G and Dauchot O 2005 Phys. Rev. Lett. 94 015701
7. Liu B and Goree J 2007 Phys. Rev. E 75 016405
8. Gorenflo R and Mainardi F 1997 Fractals and Fractional Calculus in Continuum Mechanics ed A Carpinteri and F Mainardi (Wien: Springer) p 223 http://www.fracalmo.org
9. Mainardi F, Luchko Y and Pagnini G 2001 Frac. Cal. Appl. Anal. 4 153 http://arxiv.org/abs/cond-mat/0702419
10. Podlubny I 1999 Fractional Differential Equations (San Diego: Academic)
11. Schneider W R 1990 Dynamics and Stochastic Processes, Theory and Applications (Lecture Notes in Physics vol 355) ed R Lima et al (Heidelberg: Springer) p 276
12. Schneider W R and Wyss W 1989 J. Math. Phys. 30 134
13. Revuz D and Yor M 1994 Continuous Martingales and Brownian Motion (A Series of Comprehensive Studies in Mathematics vol 293) (Berlin: Springer)
14. Molchanov S A and Ostrovskii E 1969 Theory Probab. Appl. 14 128
15. Mainardi F 1996 Chaos, Solitons Fractals 7 1461
16. Mainardi F 1997 Fractals and Fractional Calculus in Continuum mechanics ed A Carpinteri and F Mainardi (Wien New York: Springer) p 291 http://www.fracalmo.org
17. Kolsrud T 1990 Ideas and Methods in Mathematical Analysis, Stochastics and Applications vol 1 ed S Albeverio et al (Cambridge: Cambridge University Press) p 168
18. Donati-Martin C, Roynette B, Vallois P and Yor M 2008 Stud. Sci. Math. Hung. 45 ((2)) 207-21 DOI:10.1556/SScMath.2007.1033
19. Meerschaert M, Benson D, Scheffler H and Baeumer B 2002 Phys. Rev. E 65 041103
20. Metzler R and Klafter J 2000 Phys. Rep. 339 1
21. Barkai E 2002 Chem. Phys. 284 13
22. Gorenflo R and Mainardi F 2008 Anomalous Transport: Foundations and Applications ed R Klages et al (Weinheim: Wiley-VCH) http://arxiv.org/abs/0705. 0797
23. Stanislavsky A A 2003 Phys. Scr. 67 265
24. Fulger D, Scalas E and Germano G 2008 Phys. Rev. E 77 021122
25. Bochner S 1955 Harmonic Analysis and the Theory of Probability (Berkeley, CA: University of California Press)
26. Bochner S 1962 Proc. Natl Acad. Sci. USA 48 19
27. Mura A and Mainardi F 2008 submitted http://arxiv.org/abs/0711.0665
28. Taqqu M S 2003 Theory and Applications of Long-Range Dependence ed P Doukhan et al (Basle: Birkäuser) p 5
29. Schneider W R 1990 Stochastic Processes, Physics and Geometry ed S Albeverio et al (Singapore: World Scientific) p 676
30. Schneider W R 1990 Ideas and Methods in Mathematical Analysis, Stochastics and Applications vol 1 ed S Albeverio et al (Cambrdige: Cambridge University Press) p 261
31. Mandelbrot B B 1976 J. Hydrol. 30 407
32. Mandelbrot B B and Van Ness J W 1968 SIAM Rev. 10 422
33. Schneider W R 1996 Exposition. Math. 14 3
34. Gorenflo R, Mainardi F, Moretti D and Paradisi P 2002 Nonlinear Dyn. 29 129
35. Gorenflo R, Mainardi F, Moretti D, Pagnini G and Paradisi P 2002 Chem. Phys. 284 521
36. Bardet J, Lang G, Oppenheim G, Philippe A and Taqqu M S 2003 Theory and Applications of Long-Range Dependence ed P Doukan et al (Basle: Birkäuser) p 579
37. Mainardi F 1996 Appl. Math. Lett. 9 23