Lévy stable processes. From stationary to self-similar dynamics and back. An application to finance

Acta Physica Polonica B

Volumn 35, Issue 4, 2004, Pages 1343-1358

  Burnecki, Krzysztof ^a   Weron, Aleksander ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN MOVEMENT; DIFFERENTIAL EQUATIONS; DIFFUSION; FINANCE; FINANCIAL DATA PROCESSING; GAUSSIAN NOISE (ELECTRONIC); MATHEMATICAL TRANSFORMATIONS; PHYSICAL PROPERTIES;

ANOMALOUS DIFFUSION; ERGODIC THEORY; FINANCIAL MODELING; STOCHASTIC INTEGRAL DESCRIPTION;

DYNAMIC PROGRAMMING;

EID: 2442716395     PISSN: 05874254     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (30)

1. P. Erabrechts, M. Maejima, Selfsimilar Processes, Princeton University Press, Princeton 2002.
2. C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger, Phys. Rev. E49, 1685 (1994).
3. Sz. Mercik, K. Weron, Z. Siwy, Phys. Rev. E60, 7343 (1999).
4. I. Eliazar, J. Klafter, J. Stat. Phys. 111, 739 (2003).
5. A. Chechkin, J. Klafter, I.M. Sokolov, Europhys. Lett. 63, 326 (2003).
6. S. Picozzi, B.J. West, Phys. Rev. E66, 046118 (2002).
7. Sz. Mercik, K. Weron, Phys. Rev. E63, 051910 (2001).
8. S. Bovelli, D. Fioretto, A. Jurlewicz, J. Phys.: Condens. Matter 13, 373 (2001).
9. R. Weron, Intern. J. Modern Phys. C12, 209 (2001); Physica A 312, 285 (2002).
10. R. Weron, Intern. J. Modern Phys. C12, 209 (2001); Physica A 312, 285 (2002).
11. Sz. Mercik, K. Weron, K. Burnecki, A. Weron, Acta Phys. Pol. B 34, 3773 (2003).
12. A. Janicki, A. Weron, A Simulation and Chaotic Behaviour of α-Stable Stochastic Processes, Marcel Dekker Inc., New York 1994.
13. G. Samorodnitsky, M.S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall, London 1994.
14. C. Tsallis, S.V.F. Levy, A.M.C. Souza, R. Maynard, Phys. Rev. Lett. 75, 3589 (1995); 77, 5442 (1996).
15. C. Tsallis, S.V.F. Levy, A.M.C. Souza, R. Maynard, Phys. Rev. Lett. 75, 3589 (1995); 77, 5442 (1996).
16. J.W. Lamperti, Trans. Amer. Math. Soc. 104, 62 (1962).
17. R.J. Adler, S. Cambanis, G. Samorodnitsky, Stoch. Proc. Appl. 34, 1 (1990).
18. K. Burnocki, J. Rosiński, A. Weron, in Stochastic Processes & Related Topics, eds. I. Karatzas et al., Birkhäuser, Boston 1998, p. 1.
19. U. Krengel, Ergodic Theorems, De Gruyter, Berlin 1985.
20. M. Maejima, Sugaku Expositions 2, 102 (1989).
21. K. Burnecki, M. Maejima, A. Weron, Yokohama Math. J. 44, 25 (1997).
22. A. Makagon, H. Salehi, in Stochastic Processes, eds. S. Cambanis et al., Springer-Verlag, New York 1993, p. 245.
23. M. Maejima, K. Sato, J. Theoret. Prob. 12, 347 (1999).
24. S. Mittnik, S.T. Rachev, Stable Paretian Models in Finance, Wiley & Sons, 2000.
25. P. Embrechts, C. Klüppelberg, T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin 1997.
26. J.P. Bouchaud, D. Sornette, J. Phys. France 4, 863 (1994).
27. L.C.G. Rogers. Math. Finance 7, 95 (1997).
28. W. Dai, C.C. Heyde, J. Appl. Math. Stochastic Anal. 9, 439 (1996).
29. W. Willinger, M.S. Taqqu, W. E. Leland, D.V. Wilson, Statistical Science 10, 67 (1995).
30. I. Norros, E. Valkeila, J. Virtamo, Bernoulli 5, 571 (1999).