Fractional stable distributions

Journal of Mathematical Sciences

Volumn 105, Issue 6, 2001, Pages 2569-2576

  Kolokoltsov, V ^a,b   Korolev, V ^a,c   Uchaikin, V ^a,d  

^a Nottingham Trent University ^*

^b NOTTINGHAM TRENT UNIVERSITY   (United Kingdom)

^c MOSCOW STATE UNIVERSITY   (Russian Federation)

^d ULYANOVSK STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 20444380630     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1023/A:1011359219202     Document Type: Article

References (22)

1. O. E. Barndorff-Nielsen, Gaussian\\Inverse Gaussian Processes and the Modeling of Stock Returns, Preprint, Aarhus University, Aarhus (1994).
2. G. M. Batanov, "Statistical properties and radial structure of plasma turbulence in the boundary region of the L2-M stellarator," Plasma Phys. Control. Fusion, 40, 1241-1250 (1998).
3. J. T. Bendler and M. F. Shlesinger, in: The Wonderful World of Stochastics, North-Holland, Amsterdam (1985).
4. J.-P. Bouchaud and A. Georges, "Anomalous diffusion in disordered media: statistical mechanics, models, and physical applications," Phys. Rep., 145, 127-293 (1990).
5. M. B. Isichenko, "Percolation, statistical topography, and transport in random media," Rev. Mod. Phys., 64, 9611043 (1992).
6. B. V. Gnedenko and V. Yu. Korolev, Random Summation: Limit Theorems and Applications, CRC Press, Boca Raton, Florida (1996).
7. J. Klafter, A. Blumen, and M. F. Shlesinger, Phys. Rev., A, 35, 3081 (1987).
8. J. Klafter, G. Zumofen, and M. F. Shlesinger, Physica, A, 200, 222 (1993).
9. V. Yu. Korolev, "A general theorem on the limit behavior of superpositions of independent random processes with applications to Cox processes," J. Math. Sci., 81, No. 5, 2951-2956 (1996).
10. M. Kotulski, "Asymptotic distributions of the continuous-time random walks: a probabilistic approach," J. Stat. Phys., 81, 777-779 (1995).
11. V. M. Kruglov and V. Yu. Korolev, Limit Theorems for Random Sums [in Russian], Moscow State Univ. Press, Moscow (1990).
12. R. Metzler, E. Barkai, and J. Klafter, "Anomalous transport in disordered systems under the influence of external fields," Physica, A, 266, 343-350 (1999).
13. E. W. Montroll and G. H. Weiss, J. Math. Phys., 6, 167 (1965).
14. G. Samorodnitsky and M. S. Taqqu, Stable Non Gaussian Random Processes, Stochastic Models with Infinite Variance, Chapman and Hall, New York (1994).
15. H. Scher and M. Lax, Phys. Rev., B, 7, 4491 (1973).
16. M. F. Shlesinger, B. J. West, and J. Klafter, Phys. Rev. Lett., 58, 1110 (1987).
17. M. F. Shlesinger, J. Stat. Phys., 36, 639 (1984).
18. V. V. Uchaikin and V. M. Zolotarev, Chance and Stability: Stable Distributions and Their Applications, VSP, Utrecht, The Netherlands (1999).
19. G. H. Weis and R. J. Rubin, Adv. Chem. Phys., 52, 363 (1983).
20. B. J. West and W. Deering, "Fractal physiology for physicists: Lévy statistics," Phys. Rep., 246, 1-100 (1994).
21. V. M. Zolotarev, One-Dimensional Stable Distributions, Amer. Math. Soc., Providence, RI (1986).
22. G. Zumofen, J. Klafter, and A. Blumen, Phys. Rev., E, 47, 2183 (1993).