Fractional Lévy motions and related processes

Journal of Physics A: Mathematical and General

Volumn 32, Issue 42, 1999, Pages 7225-7248

  Huillet, Thierry ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033595655     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/42/301     Document Type: Article

References (46)

1. Aharony A and Feder J (ed) 1989 Fractals in physics Physica D 38 1-3
2. Ball C A (ed) 1993 A review of stochastic volatility models with applications to option pricing Financial Markets, Institutions and Instruments vol 2 (Cambridge: Blackwell) pp 55-71
3. Benassi A, Cohen S and Istas J 1998 Identifying the multifractional function of a Gaussian process Stat. Prob. Lett. 39 337-45
4. Bhattacharya R N, Gupta V K and Waymire E 1983 The Hurst effect under trends J. Appl. Prob. 20 649-62
5. Bouchaud J-P and Georges A 1990 Anomalous diffusion in disordered media: statistical mechanics models and physical applications Phys. Rep. 195 12 Bouchaud J-P and Georges A 1990 Phys. Rep. 195 127-293
6. Bouchaud J-P and Georges A 1990 Anomalous diffusion in disordered media: statistical mechanics models and physical applications Phys. Rep. 195 12 Bouchaud J-P and Georges A 1990 Phys. Rep. 195 127-293
7. Clark P K 1973 A subordinated stochastic process model with finite variance for speculative prices Econometrica 41 135-55
8. Embrechts P, Klüppelberg C and Mikosh T 1997 Modelling extremal events Applications of Mathematics vol 33 (Berlin: Springer)
9. Feller W 1971 An Introduction to Probability Theory and its Applications vol 1 (New York: Wiley) Feller W 1971 An Introduction to Probability Theory and its Applications vol 2 (New York: Wiley)
10. Feller W 1971 An Introduction to Probability Theory and its Applications vol 1 (New York: Wiley) Feller W 1971 An Introduction to Probability Theory and its Applications vol 2 (New York: Wiley)
11. Galambos J 1978 The Asymptotic Theory of Extreme Order Statistics (New York: Wiley)
12. Gnedenko B V and Kolmogorov A N 1954 Limit Distributions for Sums of Independent Random Variables (Cambridge: Addison-Wesley)
13. Gumbel E J 1958 Statistics of Extremes (Columbia: Columbia University Press)
14. Huillet T and Jeannet B 1998 Multifractal formalism for self-similar bridges J. Phys. A: Math. Gen. 31 2567-90
15. Hurst H E 1951 Long-term storage capacity of reservoirs Trans. Am. Soc. Civil Engng 116 770-808
16. Jespersen S, Metzler R and Fogedby H C 1999 Lévy flights in external force fields: Langevin and fractional Fokker-Planck equations and their solutions Phys. Rev. E 39 2736-45
17. Kotulski M 1995 Asymptotic distributions of the continuous time random walks: a probabilistic approach J. Stat. Phys. 81 777-92
18. Klafter J, Schlesinger M F and Zumofen G 1996 Beyond Brownian motion Phys. Today 49 33-9
19. Klafter J and Schlesinger M F 1994 Probability distributions for continuous-time random walks with long tails J. Phys. Chem. 98 7366-70
20. Kusnezov D, Bulgac A and Do Dang G 1998 Quantum Lévy processes and fractional kinetics Preprint 98-75. LPTHE U Paris Sud
21. Lamperti J W 1962 Semi-stable stochastic processes Trans. Am. Math. Soc. 104 62-78
22. Lévy P 1937 Théorie de L'addition des Variables Aléatoires (Paris: Gauthier-Vilars)
23. Lukacs E 1983 Developments in Characteristic Function Theory (London: Griffin)
24. Mandelbrot B B and Van Ness J W 1968 Fractional Brownian motions, fractional noises and applications SIAM Rev. 10 422-37
25. Mandelbrot B B and Wallis J R 1969 Computer experiments with fractional Gaussian noises, part 1: averages and variances Water Resour. Res. 5 228-41
26. Mandelbrot B B and Wallis JR 1969 Computer experiments with fractional Gaussian noises, part 2: rescaled range and spectra Water Resour. Res. 5 242-59
27. Mandelbrot B B and Wallis J R 1969 Computer experiments withfractional Gaussian noises, part 3: mathematical appendix Water Resour. Res. 5 260-5
28. Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)
29. Mandelbrot B B 1997 Fractales, Hasard et Finance (Paris: Flammarion)
30. Mandelbrot BB 1997 Fractals and Scaling in Finance; Discontinuity, Concentration, Risk (Berlin: Springer)
31. Mandelbrot B B 1973 Comments on 'A subordinated stochastic process model with finite variance for speculative prices' by Peter K Clark Econometrica 41 157-9
32. Mandelbrot B B, Fisher A and Calvet L 1997 A multifractal model of asset returns Cowles Foundation discussion paper 1164
33. Montroll E W and Weiss G H 1965 Random walks on lattices. II J. Math. Phys. 6 167-81
34. Montroll E W and Shlesinger M F 1983 Maximum entropy formalism, fractals, scaling phenomena, and 1/f noise: a tale of tails J. Stat. Phys. 32 209-30
35. Pareto V 1965 Cours d'Economie Politique (1896) reprinted as a volume of Oeuvres Complètes (Geneva: Droz)
36. Peltier R F and Lévy-Vehel J 1995 Multifractional Brownian motion: definition and preliminary results INRIA Report 2645
37. Samorodnisky G and Taqqu M 1994 Stable Non-Gaussian Processes: Stochastic Models with Infinite Variance (New York: Chapman and Hall)
38. Schlesinger M F, Zaslavsky G M and Frisch U (ed) 1994 Lévy flights and related topics in physics (Lecture Notes in Physics vol 450) (Berlin: Springer)
39. Schlesinger M F, Zaslavsky G M and Klafter J 1993 Strange kinetics Nature 363 31-7
40. Taqqu M S and Wolpert R 1983 Infinite variance self-similar processes subordinate to a Poisson measure Z. Wahrscheinlichkeitstheor. Verwandte Geb. 62 53-72
41. Tsallis C, Lévy S V F, Souza A M C and Maynard R 1995 Statistical-mechanics foundation of the ubiquity of Lévy distributions in physics Phys. Rev. Lett. 75 3589-93
42. Tsallis C 1995 Nonextensive thermostatistics: brief review and comment Physica A 221 277-90
43. Van Kampen N G 1981 Stochastic Processes in Physics and Chemistry (Amsterdam: North Holland)
44. Wax N (ed) 1954 Selected Papers on Noise and Stochastic Processes (New York: Dover)
45. Weissmann H, Weiss G H and Havlin S 1989 Transport properties of the continous-time random walk with a long-tailed waiting time density J. Stat. Phys. 57 301-16
46. Zipf G K 1949 Human Behaviour and the Principle of Least Effort (Reading, MA: Addison-Wesley)