Montroll-Weiss problem, fractional equations, and stable distributions

International Journal of Theoretical Physics

Volumn 39, Issue 8, 2000, Pages 2087-2105

  Uchaikin, Vladimir V ^a  

^a ULYANOVSK STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034348080     PISSN: 00207748     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1003670023058     Document Type: Article

References (38)

1. V. V. Afanasiev, R. Z. Sagdeev, and G. M. Zaslavsky, (1991). Chaos 1(2), 143.
2. V. Balakrishnan, (1985). Physica A 132, 569.
3. E. Barkai, R. Metzler, and J. Klafter, (2000). Phys. Rev. E 61, 192.
4. L. N. Bol'shev, V. M. Zolotarev, E. S. Kedrova and M.A. Rybinskaya, (1968). Theor. Probability Appl. 15, 299.
5. J.-P. Bouchaud, and A. Georges, (1990). Phys. Rep. 195, 127.
6. A. Compte, (1996). Phys. Rev. E 53, 4191.
7. A. Compte, D. Jou, and Y. Katayama, (1997). J. Phys. A: Math. Gen. 30, 1023.
8. H. E. Daniels, (1954). Ann. Math. Phys. 25, 631.
9. E. F. Fama, and R. Roll. (1968). J. Amer. Statist. Assoc. 63, 817.
10. W. Feller, (1971). An Introduction to Probability Theory. Vol. 2 (Wiley, New York).
11. C. Fox, (1961). Trans. Am. Math. Soc. 98, 395.
12. R. Hilfer, (1995). Fractals 3, 211.
13. D. R. Holt and E. L. Crow, (1973). J. Res. NBS-B. Math. Sci. 77B, 143.
14. M. B. Isichenko, (1992). Rev. Mod. Phys. 64, 961.
15. Yu. L. Klimontovich, (1995). Statistical Theory of Opened Systems, Kluwer, Dordrecht.
16. M. Kotulski, (1995). J. Stat. Phys. 81, 771.
17. F. Mainardi, P. Paradisi, and R. Gorenflo, (1999). In Econophysics: An Emerging Science, J. Kertesz and I. Kondor, eds., Kluwer, Dordrecht, in press, pp. 39.
18. A. M. Mathai and R. K. Saxena, (1973). Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Lect. Not. Math. 348, (Springer Verlag, Heidelberg).
19. K. S. Miller and B. Ross, (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, (Wiley, New York).
20. A. S. Monin, (1955). Doklady Akad. Nauk SSSR 105, 256 (in Russian).
21. E. W. Montroll and G. H. Weiss, (1965). J. Math. Phys. 6, 167.
22. R. R. Nigmatullin, (1986). Phys. Stat. Sol (b) 133, 425.
23. K. B. Oldham and J. Spanier, (1974). The Fractional Calculus, (Academic Press, New York).
24. A. I. Saichev and G. M. Zaslawsky, (1997). Chaos 7(4), 753.
25. S. G. Samko, A. A. Kilbas, and O. I. Marichev, (1993). Fractional Integrals and Derivatives -Theory and Applications, (Gordon and Breach, New York).
26. W. R. Schneider, (1986). Lecture Notes in Physics, Vol. 262, Springer, Berlin, 497.
27. W. R. Schneider and W. Wyss, (1989). J. Math. Phys. 30, 134.
28. M. F. Shlesinger, J. Klafter, and Y. M. Wong, (1982). J. Stat. Phys. 27(3).
29. H. M. Srivastava, K. C. Gupta, and S. P. Goyal, (1982). The H-Functions of One and Two Variables with Applications, (South Asian Publishers, New Delhi).
30. J. K. E. Tunaley, (1974). J. Stat. Phys. 11, 397.
31. V. V. Uchaikin and V. M. Zolotarev, (1999). Chance and Stability. Stable Distributions and their Applications, (VSP, Utrecht, The Netherlands).
32. H. Weissman, G. H. Weiss, and S. Havlin, (1989). J. Stat. Phys. 57, 301.
33. B. J. West and W. Deering, (1994). Phys. Rep. 246, 1.
34. B. J. West, P. Grigolini, R. Metzler, and T. F. Nonnenmacher, (1997). Phys. Rev. E 55, 100.
35. G. J. Worsdale and J. Roy, (1975). Statist. Soc. Ser. C: Appl. Statist. 24, 123.
36. W. Wyss, (1986). J. Math. Phys. 27, 2782.
37. G. M. Zaslavsky, (1994). Physica D 76, 110.
38. V. M. Zolotarev, (1981). In Contribution to Probability (Collection Dedicated to Eugene Lukass), eds. J. Gani and V. K. Rohatgi, Academic Press, London, 283.