Memory effects in fractional Brownian motion with Hurst exponent H<1/3

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

Volumn 82, Issue 2, 2010, Pages

  Bologna, Mauro ^a   Vanni, Fabio ^b   Krokhin, Arkadii ^b   Grigolini, Paolo ^b  

^a UNIVERSIDAD DE TARAPACÁ   (Chile)

^b UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FRACTIONAL BROWNIAN MOTION; HURST EXPONENTS; INVERSE POWER LAW; MEMORY EFFECTS; POWER INDICES;

BROWNIAN MOVEMENT;

EID: 77956106393     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.020102     Document Type: Article

References (19)

1. B. B. Mandelbrot and J. W. Van Ness, SIAM Rev. 10, 422 (1968). 10.1137/1010093
2. J. Feder, Fractals (Plenum Press, New York, 1988).
3. J. Beran, Statistics for Long-Memory Processes (Chapman and Hall, New York, 1994).
4. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). 10.1016/S0370- 1573(00)00070-3
5. M. Magdziarz, A. Weron, K. Burnecki, and J. Klafter, Phys. Rev. Lett. 103, 180602 (2009). 10.1103/PhysRevLett.103.180602
6. J.-H. Jeon and R. Metzler, Phys. Rev. E 81, 021103 (2010). 10.1103/PhysRevE.81.021103
7. C. Godrèche, S. N. Majumdar, and G. Schehr, Phys. Rev. Lett. 102, 240602 (2009). 10.1103/PhysRevLett.102.240602
8. R. García-García, A. Rosso, and Grégory Schehr, Phys. Rev. E 81, 010102 (R) (2010). 10.1103/PhysRevE.81.010102
9. M. Ding and W. Yang, Phys. Rev. E 52, 207 (1995). 10.1103/PhysRevE.52.207
10. G. Rangarajan and M. Ding, Phys. Lett. A 273, 322 (2000). 10.1016/S0375-9601(00)00518-1
11. G. M. Molchan, Commun. Math. Phys. 205, 97 (1999). 10.1007/s002200050669
12. J. Krug and H. T. Dobbs, Phys. Rev. Lett. 76, 4096 (1996). 10.1103/PhysRevLett.76.4096
13. R. Failla, P. Grigolini, M. Ignaccolo, and A. Schwettmann, Phys. Rev. E 70, 010101 (R) (2004). 10.1103/PhysRevE.70.010101
14. J. Krug, H. Kallabis, S. N. Majumdar, S. J. Cornell, A. J. Bray, and C. Sire, Phys. Rev. E 56, 2702 (1997). 10.1103/PhysRevE.56.2702
15. R. Cakir, P. Grigolini, and A. A. Krokhin, Phys. Rev. E 74, 021108 (2006). 10.1103/PhysRevE.74.021108
16. G. H. Weiss, Aspects and Applications of the Random Walk (North Holland Press, Amsterdam, 1994).
17. S. Redner, A Guide to First-Passage Time Processes (Cambridge University Press, New York, 2001). 10.1017/CBO9780511606014
18. 1 (u) ≡ ψ̂ (u) and also that ψ̂ 0 (t) =δ (t), one obtains Eq. d11.
19. U. Kuhl, F. M. Izrailev, A. A. Krokhin, and H. J. Stöckmann, Appl. Phys. Lett. 77, 633 (2000). 10.1063/1.127068