Crossover between Lévy and Gaussian regimes in first-passage processes

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 76, Issue 2, 2007, Pages

  Inoue, Jun Ichi ^a   Sazuka, Naoya ^b  

^a HOKKAIDO UNIVERSITY   (Japan)

^b SONY CORPORATION   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DISTRIBUTION FUNCTIONS; RANDOM PROCESSES; SCALING LAWS;

CROSSOVER POINT; EFFECTIVE CUTOFF LENGTH; FIRST-PASSAGE TIME DISTRIBUTION;

PROBLEM SOLVING;

EID: 34548087283     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.021111     Document Type: Article

References (30)

1. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, England, 2001).
2. N. G. van Kappen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
3. H. C. Tuckwell, Introduction to Theoretical Neurobiology (Cambridge University Press, Cambridge, England, 1988), Vol. 2.
4. H. C. Tuckwell, Stochastic Processes in the Neurosciences (Society for Industrial and Applied Mathematics, Philadelphia, 1989).
5. I. Simonsen, M. H. Jensen, and A. Johansen, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2002-00193-x 27, 583 (2002).
6. M. Raberto, E. Scalas, and F. Mainardi, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)01048-8 314, 749 (2002).
7. E. Scalas, R. Gorenflo, H. Luckock, F. Mainardi, M. Mantelli, and M. Raberto, Quant. Finance ZZZZZZ 1469-7688 4, 695 (2004).
8. S. Kurihara, T. Mizuno, H. Takayasu, and M. Takayasu, The Application of Econophysics, edited by, H. Takayasu, (Springer, New York, 2003), pp. 169-173.
9. T. Kaizoji and M. Kaizoji, Physica A PHYADX 0378-4371 10.1016/j.physa.2003.12.054 336, 563 (2004).
10. E. Scalas, Physica A PHYADX 0378-4371 362, 225 (2006).
11. N. Sazuka, Eur. Phys. J. B EPJBFY 1434-6028 50, 129 (2006).
12. N. Sazuka, Physica A PHYADX 0378-4371 376, 500 (2007).
13. http://moneykit.net/
14. G. Rangarajan and M. Ding, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.120 62, 120 (2000).
15. R. N. Mantegna and H. E. Stanley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.2946 73, 2946 (1994).
16. R. N. Mantegna, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.49.4677 49, 4677 (1994).
17. I. Koponen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.52.1197 52, 1197 (1995).
18. G. Rangarajan and M. Ding, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00518-1 273, 322 (2000).
19. G. Rangarajan and M. Ding, Fractals FRACEG 0218-348X 10.1142/ S0218348X00000159 8, 139 (2000).
20. R. Durrett, Essentials of Stochastic Processes (Springer-Verlag, New York, 1999).
21. R. Chikara and L. Folks, The Inverse Gaussian Density (Dekker, New York, 1989).
22. W. Gerstner and W. Kistler, Spiking Neuron Models (Cambridge University Press, Cambridge, England, 2002).
23. H. Risken, The Fokker-Plank Equation: Methods of Solution and Applications (Springer-Verlag, Berlin, 1989).
24. C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1983).
25. K. Umeno, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.2644 58, 2644 (1998).
26. W. Schoutens, Lévy Processes in Finance: Pricing Financial Derivatives (Wiley, New York, 2003).
27. S. I. Boyarchenko and S. Z. Levendorskii (unpublished).
28. R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, England, 2000).
29. J. Voit, The Statistical Mechanics of Financial Markets (Springer, New York, 2001).
30. T. Koren, A. V. Chechkin, and J. Klafter, Physica A PHYADX 0378-4371 379, 10 (2007).