Lévy, ornstein-uhlenbeck, and subordination: Spectral vs. Jump description

Journal of Statistical Physics

Volumn 119, Issue 1-2, 2005, Pages 165-196

  Eliazar, Iddo ^a   Klafter, Joseph ^b  

^a BAR ILAN UNIVERSITY   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

L vy driven Ornstein Uhlenbeck dynamics; Non Brownian L vy motions; Poisson superposition; Selfsimilar L vy motions; Temporal L vy subordination

Indexed keywords

EID: 18644379335     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-004-2710-9     Document Type: Article

References (57)

1. P. Lévy, Calcul des Probabilités (Gauthier-Villars, 1925).
2. P. Lévy, Théorie de l'addition des variables Alé atoires (Gauthier-Villars, 1954).
3. P. Lévy, Processus Stochastiques et mouvement Brownien (Gauthier-Villars, 1965).
4. B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for Sums of Independent Random Variables (Addison-Wesley, 1954).
5. I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Sequences of Random Variables (Walterss-Noordhoff, 1971).
6. V. M. Zolotarev, One-Dimensional Stable Distributions (AMS, 1986).
7. G. Samrodintsky and M. S. Taqqu, Stable Non-Gaussian Random Processes (CRC Press, 1994).
8. J. Bertoin, Lévy Processes (Cambridge Univercity Press, 1996).
9. J. Bertoin, One-sided Lévy Motions: Examples and Applications, Lecture Notes in Mathematics 1717, (Springer, 1999).
10. K. Sato, Lévy Processes and Infinitely Divisible Distributions (Cambridge University Press, 1999).
11. V V. Uchaikin and V. M. Zolotarev, Chance and Stability, Stable Distributions and Their Applications (V.S.P. Intl. Science, 1999).
12. O. E. Barndorff-Nielsen, T. Mikosch, and S. Resnic, eds., Lévy Processes (Birkhauser, 2001).
13. P. Embrechts and M. Maejima, Selfsimilar Processes (Princeton University Press, 2002).
14. T. Solomon, E. Weeks, H. Swinney, Phys. Rev. Lett. 71:3975 (1993).
15. A. V. Chechkin, V Y. Gonchar, M. Szydlowsky, Phys. Plasma 9:78 (2002).
16. R. P. D. Atkinson, C. J. Rhodes, D. W. Macdonald, and R. M. Anderson, OIKOS 98:134 (2002).
17. M. Levandowsky, B.S. White, and F. L. Schuster, Acta Protozool. 36:237 (1997).
18. A. W. Visser and U. H. Thygesen, J. Plankton Res. 25:1157 (2003).
19. K. Ito, Selected Papers D. W. Strook and S. R. S. Varadhan eds., (Springer, 1987).
20. K. Ito, On Stochastic Differential Equations, (AMS, 1951).
21. K. Ito and H.P. McKean, Diffusion Processes and Their Sample Paths (Springer 1974).
22. K. Ito, Lectures on Stochastic Processes (Springer, 1985).
23. H. P. McKean, Stochastic Integrals, (Academic Press, 1969).
24. Z. Schuss, Theory and Applications of Stochastic Differential Equations (John Wiley, 1980).
25. B. K. Oksendal, Stochastic Differential Equations (Springer, 1998).
26. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed. (Springer, 1991).
27. M. F. Shlesinger, J. Klafter, Y. M. Wong, J. Stat. Phys., 27:499 (1982).
28. F. E. Peseckis, Phys. Rev. A 36(2):892 (1987).
29. J. P. Bouchaud and A. Georges, Phys. Rep. 195:12 (1990).
30. M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature 363:31 (1993).
31. H. C. Fogedby, Phys. Rev. E 50(2):1657 (1994).
32. M. F. Shlesinger, G. M. Zaslavsky, and U. Frisch (eds.), Levy Flights and Related Topics (Springer, 1995).
33. R. N. Mantegna and H. E. Stanley, Nature 376:46 (1995).
34. R. N. Mantegna and H. E. Stanley, Nature 383:587 (1996).
35. J. Klafter, M. F. Shlesinger, and G. Zumofen, Phys. Today 49(2):33 (1996).
36. A. I. Saichev and G. M. Zaslavsky, Chaos 7:753 (1997).
37. S. Jespersen, R. Metzler, and H. C. Fogedby, Phys. Rev. E 59(3):2736 (1999).
38. R. Metzler and J. Klafter, Phys. Rep. 339:1 (2000).
39. A. Chechkin, V. Gonchar, J. Klafter, R. Metzler, and L. Tantarov, Chem. Phys. (in press).
40. C. K. Peng, J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley, and A. L. Goldberger, Phys. Rev. Lett. 70:1343 (1993).
41. R. Segev, M. Benveniste, E. Hulata, N. Cohen, A. Palevski, E Kapon, Y. Shapira, and E. Ben-Jacob, Phys. Rev. Lett. 88:118102 (2002).
42. O. Sotolongo-Costa, J. C. Antoranz, A. Posadas, F. Vidal, and A. Vazquez, Geophys. Rev. Lett. 27:1965 (2000).
43. S. A. Kassam, Signal Detection in Non-Gaussian Noise, (Springer, 1988).
44. E. J. Wegman, S. C. Schwartz, and J.B. Thomas, eds., Topics in Non-Gaussian Signal Processing (Springer, 1989).
45. C. L. Nikias and M. Shao, Signal Processing with Alpha-Stable Distributions and Applications (John Wiley, 1995).
46. R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics (Cambridge University Press, 2000).
47. J. P. Bouchaud, M. Potters, Theory of Financial Risk (Cambridge University Press, 2000).
48. B. Mandelbrot, Fractals and Scaling in Finance, (Springer, 1997).
49. I. M. Sokolov, J. Klafter, and A. Blumen, Phys. Today 55:48 (2002).
50. I. Eliazar and J. Klafter, J. Stat. Phys. 111(314):739 (2003).
51. I. Eliazar and J. Klafter, Physica A 330:17 (2003); cond-mat 0307308.
52. I. Eliazar and J. Klafter, Physica A 336:219 (2004).
53. W. Feller, An Introduction to Probability Theory and Its Applications Vol. 2, 2nd edn., (John Wiley, 1971).
54. I. M. Sokolov, Phys. Rev. E 63:011104 (2000).
55. I. Eliazar, J. Klafter, Physica D 187:30 (2004).
56. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed., (Academic Press, 1994).
57. B. B. Mandelbrot and R. L. Hudson, The (mis)Behavior of Markets (basic Books, 2004).