Subdiffusion and stable laws

Journal of Experimental and Theoretical Physics

Volumn 88, Issue 6, 1999, Pages 1155-1163

  Uchaikin V V ^a  

^a ULYANOVSK STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22644449238     PISSN: 10637761     EISSN: None     Source Type: Journal    
DOI: 10.1134/1.558905     Document Type: Article

References (31)

1. J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).
2. M. B. Isichenko, Rev. Mod. Phys. 64, 961 (1992).
3. B. J. West and W. Deering, Phys. Rep. 246, 1 (1994).
4. V. M. Zolotarev, V. V. Uchaǐkin, and V. V. Saenko, Zh. Éksp. Teor. Fiz. 115, 1411 (1999)
5. [JETP 88, 780 (1999)].
6. R. R. Nigmatullin, Phys. Status Solidi B 123, 739 (1984).
7. W. Wyss, J. Math. Phys. 27 2782 (1986).
8. T. F. Nonnenmacher and D. J. F. Nonnenmacher, Acta Phys. Hung. 66, 145 (1989).
9. G. M. Zaslavsky, Physica D 76, 110 (1994).
10. K. B. Chukbar, Zh. Éksp. Teor. Fiz. 108, 1875 (1995)
11. [JETP 81, 1025 (1995)].
12. A. Compte, Phys. Rev. E 53, 4191 (1996).
13. W. R. Schneider and W. Wyss, J. Math. Phys. 30 134 (1989).
14. W. G. Glöckle and T. F. Nonnenmacher, J. Stat. Phys. 71, 741 (1993).
15. B. J. West, P. Grigolini, R. Metzler, T. F. Nonnenmacher, Phys. Rev. E 55, 99 (1997).
16. C. Fox, Trans. Am. Math. Soc. 98, 395 (1961).
17. P. Lévy, Processes stochastiques et mouvement Brownien, 2nd ed., Gauthier-Villars, Paris (1965).
18. B. V. Gnedenko and A. N. Kolmogorov, Limiting Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading, MA (1954).
19. V. M. Zolotarev, One-Dimensional Stable Distributions, American Mathematical Society, Providence, R.I. (1986).
20. W. R. Schneider, in Stochastic Processes in Classical and Quantum Systems (Proc. 1st Ascona-Como Int. Conf., held in Ascona, Ticino, Switzerland, June 24-29, 1985), S. Albeverio, G. Casati, and D. Merlini (eds.), Springer, Berlin (1986), p. 497.
21. W. R. Schneider, in Lecture Notes in Physics, Vol. 1250, Springer, Berlin (1987), p. 269.
22. W. Feller, An Introduction to the Probability Theory and Its Applications, Vol. 2, 2nd ed., Wiley, New York (1971).
23. A. A. Kilbas, O. I. Marichev, and S. G. Samko, Fractional Integrals and Derivatives: Theory and Applications, Gordon & Breach, Philadelphia (1993).
24. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York (1993).
25. A. A. Borovkov, A Course in Probability Theory [in Russian], Nauka, Moscow (1972).
26. Yu. L. Klimontovich, Statistical Theory of Open Systems, Kluwer, Dordrecht (1995).
27. E. Lukacs, Characteristic Functions, Hafner, New York (1970).
28. H. Scher and E. W. Montroll, Phys. Rev. E 12, 2455 (1975).
29. V. M. Zolotarev, in Proc. (Trudy) V. A. Steklov Institute of Mathematics [in Russian], Vol. 71 (1964), p. 47.
30. L. N. Bol'shev, V. M. Zolotarev, E. S. Kedrova, and M. A. Rybinskaya, Teor. Veroyatn. Primen. XV, 309 (1970).
31. D. R. Holt and E. L. Crow, J. Res. Natl. Bur. Stand., Sect. B 77B, 143 (1973).