REFERENCES
V. E. Bening and V. Yu. Korolev, "Statistical estimation of the parameters of fractional stable distributions," in: Trzydziesta Pierwsza Odnopolska Konferencia Zastosowan Matematyki, Zakopane-Koscielisko, Inst. Mat. Polsk. Akad. Nauk, Warshawa (2002), pp. 7-8.
V. E. Bening, V. Yu. Korolev, V. V. Saenko, and V. V. Uchaikin, "One-dimensional fractional stable distributions. I. Simulation and calculation. II. Estimation of parameters," in: XXIInd International Seminar on Stability Problems for Stochastic Models, Warna (2002), pp. 7-8.
J.-P. Bouchaud and A. Georges, "Anomalous dillusion in disordered media: Statistical mechanics, models, and physical applications," Phys. Rep., 195, 127-293 (1990).
M. B. Isichenko, "Percolation, statistical topography, and transport in random media," Rev. Mod. Phys., 64, 961-1043 (1992).
V. N. Kolokoltsov, "Semiclassical analysis for di_usions and stochastic processes," Lect. Notes Math., 1724 (2000).
V. N. Kolokoltsov, V. Yu. Korolev, and V. V. Uchaikin, Fractional Stable Distributions, Preprint 23/00 of Math. and Stat. Research, Nottingham Trent University (2000).
V. N. Kolokoltsov, V. Yu. Korolev, and V. V. Uchaikin, "Fractional stable distributions," J. Math. Sci., 105, 2569-2576 (2001).
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 (2001).
V. Yu. Korolev and V. V. Uchaikin, "Some limit theorems for generalized renewal processes with heavy tails," Teor. Veroyatn. Primen., 45, No. 4, 809-811 (2000).
M. Kotulskii, "Asymptotic distributions of continuous-time random walks: A probabilistic approach," J. Statist. Phys., 81, 777-779 (1995).
V. V. Uchaikin, "Multidimensional symmetric anomalous dillusion," Chem. Phys., 284, 507-520 (2002).
V. V. Uchaikin, Fractional Stable Distribution 2. Univariate densities, Preprint 12/02 of Math. and Stat. Research, Nottingham Trent University (2002).
V. V. Uchaikin and V. M. Zolotarev, Chance and Stability: Stable Distributions and Their Applications, VSP, Utrecht, The Netherlands (1999).
B. J. West and W. Deering, "Fractal physiology for physicists: Lévy statistics," Phys. Rep., 246, 1-100 (1997).
V. M. Zolotarev, One-Dimensional Stable Distributions [in Russian], Nauka, Moscow (1983).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bening, V.E., Korolev, V.Y., Kolokol'tsov, V.N. et al. Estimation of Parameters of Fractional Stable Distributions. Journal of Mathematical Sciences 123, 3722–3732 (2004). https://doi.org/10.1023/B:JOTH.0000036313.13319.cf
Issue Date:
DOI: https://doi.org/10.1023/B:JOTH.0000036313.13319.cf