Fractional brownian motion versus the continuous-time random walk: A simple test for subdiffusive dynamics

Physical Review Letters

Volumn 103, Issue 18, 2009, Pages

  Magdziarz, Marcin ^a   Weron, Aleksander ^a   Burnecki, Krzysztof ^a   Klafter, Joseph ^b,c  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b TEL AVIV UNIVERSITY   (Israel)

^c UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX SYSTEMS; CONTINUOUS-TIME RANDOM WALK; DIFFERENT PROCESS; E. COLI; FRACTIONAL BROWNIAN MOTION; FRACTIONAL FOKKER-PLANCK EQUATION; HEAVY-TAILED; HURST INDEX; MOTION OF INDIVIDUAL; MRNA MOLECULES; SUBDIFFUSIVE BEHAVIOR; WAITING TIME;

BROWNIAN MOVEMENT; EQUATIONS OF MOTION; ESCHERICHIA COLI; FOKKER PLANCK EQUATION;

CONTINUOUS TIME SYSTEMS;

EID: 70350763863     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.103.180602     Document Type: Article

References (25)

1. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3
2. G. Guigas, C. Kalla, and M. Weiss, Biophys. J. 93, 316 (2007). BIOJAU 0006-3495 10.1529/biophysj.106.099267
3. I. Golding and E.C. Cox, Phys. Rev. Lett. 96, 098102 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.098102
4. A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. Lett. 85, 5655 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.85.5655
5. W. Min, Phys. Rev. Lett. 94, 198302 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.198302
6. M.J. Saxton, Biophys. J. 92, 1178 (2007). BIOJAU 0006-3495 10.1529/biophysj.106.092619
7. B.B. Mandelbrot and J.W. Van Ness, SIAM Rev. 10, 422 (1968). SIREAD 0036-1445 10.1137/1010093
8. E. Lutz, Phys. Rev. E PLEEE8 1539-3755 64, 051106 (2001). 10.1103/PhysRevE.64.051106
9. A. Weron, K. Burnecki, Sz. Mercik, and K. Weron, Phys. Rev. E PLEEE8 1539-3755 71, 016113 (2005). 10.1103/PhysRevE.71.016113
10. A. Lubelski, I.M. Sokolov, and J. Klafter, Phys. Rev. Lett. 100, 250602 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.250602
11. R. Metzler, Acta Phys. Polon. B APOBBB 0587-4254 40, 1315 (2009).
12. Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.058101
13. T. Neusius, I.M. Sokolov, and J.C. Smith, Phys. Rev. E PLEEE8 1539-3755 80, 011109 (2009). 10.1103/PhysRevE.80.011109
14. J. Szymanski and M. Weiss, Phys. Rev. Lett. 103, 038102 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.038102
15. M.M. Meerschaert, D.A. Benson, H.P. Scheffler, and B. Baeumer, Phys. Rev. E PLEEE8 1539-3755 65, 041103 (2002). 10.1103/PhysRevE.65.041103
16. M. Magdziarz, A. Weron, and K. Weron, Phys. Rev. E PLEEE8 1539-3755 75, 016708 (2007). 10.1103/PhysRevE.75.016708
17. E. Gudowska-Nowak, B. Dybiec, P.F. Gora, and R. Zygadlo, Acta Phys. Polon. B APOBBB 0587-4254 40, 1263 (2009).
18. A. Janicki and A. Weron, Simulation and Chaotic Behaviour of α-Stable Stochastic Processes (Marcel Dekker, New York, 1994).
19. T.F. Chan and J. Shen, Image Processing. Variational, PDE, Wavelet and Stochastic Methods (SIAM, Philadelphia, 2005).
20. L.C.G. Rogers, Math. Finance 7, 95 (1997).
21. M. Magdziarz, Path Properties of Subdiffusion-A Martingale Approach, report, 2009.
22. A. Weron and M. Magdziarz, Europhys. Lett. EULEEJ 0295-5075 86, 60010 (2009). 10.1209/0295-5075/86/60010
23. J. Beran, Statistics for Long-Memory Processes (Chapman & Hall, New York, 1994).
24. Sz. Mercik, K. Weron, K. Burnecki, and A. Weron, Acta Phys. Polon. B APOBBB 0587-4254 34, 3773 (2003).
25. See EPAPS Document No. E-PRLTAO-103-028946 for the p variation test of the experimental data. For more information on EPAPS, see http://www.aip.org/ pubservs/epaps.html.