Self and spurious multi-affinity of ordinary Levy motion, and pseudo-Gaussian relations

Chaos, solitons and fractals

Volumn 11, Issue 14, 2000, Pages 2379-2390

  Chechkin, A V ^a,b   Gonchar, V Yu ^a,b  

^a KHARKOV INSTITUTE OF PHYSICS AND TECHNOLOGY   (Ukraine)

^b INSTITUTE FOR SINGLE CRYSTALS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; ESTIMATION; MATHEMATICAL MODELS; NORMAL DISTRIBUTION; STATISTICAL METHODS;

GNEDENKO LIMIT THEOREM; HURST METHOD; LEVY INDEX; ORDINARY LEVY MOTION; PSEUDO GAUSSIAN RELATIONS; SPURIOUS MULTI AFFINITY;

BROWNIAN MOVEMENT;

EID: 0034325751     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(99)00168-X     Document Type: Article

References (42)

1. Levy P. Theorie de L'addition des Variables Aleatories, Gauthier-Villiers: Paris, 1937
2. Bachelier L. Ann scientifiques de l'ecole normale superieure III. 17:1900;21.
3. Wiener N. J Math Phys. 2:1923;131.
4. Skorokhod AV. Random Processes with Independent Increments. Dordrecht: Kluwer, 1991 [in Russian, Moscow: Nauka, 1964]
5. Darling D.A. Trans Amer Math Soc. 83:1956;164.
6. Blummental R.M., Getoor R.K. Trans Amer Math Soc. 95:1960;263.
7. Blummental R.M., Getoor R.K. J Math. 4:1960;370.
8. Samorodnitsky G., Taqqu M.S. Stable non-Gaussian random processes. 1994;Chapman & Hall, New York.
9. Gnedenko BV, Kolmogorov A N. Limit Distributions for Sums of Independent Random Variables. Reading, MA: Addison-Wesley, 1954 [in Russian, Moskva: Izd-vo tekhniko-teor. lit-ry, 1949]
10. Mandelbrot B.B. The fractal geometry of nature. 1982;Freeman, New York.
11. Voss RF. In: Earnshaw RA, editor. Fundamental Algorithms in Computer Graphics. Berlin: Springer, 1985, p. 805
12. Bar'yakhtar V, Gonchar V, et al., Ukrain J Phys 1993;38:967
13. Mandelbrot B.B., Wallis J.R. Water Resour Res. 5:1969;228.
14. Rambaldi S., Pinazza O. Physica A. 208:1994;21.
15. Magre O., Guglielmi M. Chaos, Solitons & Fractals. 8:1997;377.
16. Chechkin AV, Gonchar V. Yu. Preprint cond-mat/9902209, Chaos, Solitons & Fractals, accepted
17. Mandelbrot B.B. J Business. 36:1963;394.
18. Mandelbrot B. Fractals scaling finance. 1997;Springer, Berlin.
19. Mantegna R.N. Physica A. 179:1991;232.
20. Mantegna R.N., Stanley H.E. Physica A. 254:1998;77.
21. West B.J., Deering W. Phys Rep. 246:1994;1.
22. Schlesinger M.F., West B.J., Klafter J. Phys. Rev. Lett. 58:1987;1100.
23. Schlesinger M.F., Zaslavsky G.M., Klafter J. Nature. 363:1993;31.
24. Zaslavsky G.M. Physica D. 76:1994;110.
25. Zaslavsky GM, Frisch U. In: Schlesinger MF, editor. Levy flights and related topics in physics, Proceedings of the International Workshop Held at Nice, France, 27-30 June 1994, Berlin: Springer, 1995
26. Bouchaud J.-.P., Georges A. Phys Rep. 195:1990;127.
27. Zimbardo G., Veltri P., Basile G., Principato S. Phys Plasmas. 2:1995;2653.
28. Schertzer D., Lovejoy S. Multifractals and turbulence: fundamentals and applications. 1993;World Scientific, Singapore.
29. Gorenflo R., DeFabritiis G., Mainardi F. Physica A. 269:1999;84.
30. Feder J. Fractals. 1988;Plenum Press, New York.
31. Mandelbrot BB, vanNess. SIAM Review 1968;10:422
32. Feller W. Ann Math Stat. 22:1951;427.
33. Mantegna R.N. Phys Rev E B. 5:1994;4677.
34. Umeno K. Phys Rev E. 58:1998;2644.
35. Kendall M.G., Babington S.B. Random sampling numbers. 1939;Cambridge University Press, Cambridge.
36. Chechkin AV, Gonchar V.Yu. Preprint cond-mat/9901064
37. Schmitt F., Scherzer D., Lovejoy S. Appl Stochastic Models Data Anal. 15:1999.
38. Mandelbrot B, Fisher A, Calvet L. Cowles Foundation Discussion Paper No. 1164, 1997
39. Hurst HE, Black RP, Sinaika YM. Long Term Storage in Reservoirs. An Experimental Study. London: Constable, 1965
40. Nolan J.P. Comm In Stat - Stochastic Models. 13:1997;759.
41. Meerschaert M., Scheffler H.-P. J Stat Plann Inference. 71(1-2):1998;19.
42. Bouchaud J-P, Potters M, Meyer M. Preprint cond-mat/9906347