Discriminating between normal and anomalous random walks

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

Volumn 80, Issue 6, 2009, Pages

  Dybiec, Bartłomiej ^a   Gudowska Nowak, Ewa ^a  

^a JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ANOMALOUS BEHAVIOR; ANOMALOUS DIFFUSION; ANOMALOUS TRANSPORT; CENTRAL MOMENTS; CHAPMAN-KOLMOGOROV EQUATION; DIFFUSIVE BEHAVIOR; JUMP LENGTH; LINEAR DEPENDENCE; MONTE CARLO SIMULATION; NON-GAUSSIAN; ON TIME; RANDOM WALK; STABILITY INDICES; TEMPORAL MEMORY; TIME AND SPACE; TIME DEPENDENCE; WAITING TIME;

COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; MONTE CARLO METHODS; SPECIAL EFFECTS; STABILITY CRITERIA;

EQUATIONS OF MOTION;

EID: 73649088995     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.061122     Document Type: Article

References (51)

1. J. P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990). 10.1016/0370-1573(90)90099-N
2. A. A. Dubkov, B. Spagnolo, and V. V. Uchaikin, Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, 2649 (2008). 10.1142/S0218127408021877
3. Lévy Flights and Related Topics in Physics, edited by, M. F. Shlesinger, G. M. Zaslavsky, and, J. Frisch, (Springer, Berlin, 1995). 10.1007/3-540-59222-9
4. R. Metzler and J. Klafter, J. Phys. A 37, R161 (2004). 10.1088/0305-4470/37/31/R01 (Pubitemid 39063557)
5. G. M. Viswanathan, Nature (London) 381, 413 (1996). 10.1038/381413a0
6. D. W. Sims, Nature (London) 451, 1098 (2008). 10.1038/nature06518 (Pubitemid 351317439)
7. A. M. Reynolds and C. J. Rhodes, Ecology 90, 877 (2009). 10.1890/08-0153.1
8. A. M. Edwards, Nature (London) 449, 1044 (2007). 10.1038/nature06199 (Pubitemid 350017586)
9. J. Klafter, A. Blumen, and M. F. Shlesinger, Phys. Rev. A 35, 3081 (1987). 10.1103/PhysRevA.35.3081
10. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). 10.1016/S0370- 1573(00)00070-3
11. G. Zumofen and J. Klafter, Phys. Rev. E 51, 1818 (1995). 10.1103/PhysRevE.51.1818
12. J. L. Doob, Ann. Math. 43, 351 (1942). 10.2307/1968873
13. A. Janicki and A. Weron, Simulation and Chaotic Behavior of α -Stable Stochastic Processes (Marcel Dekker, New York, 1994).
14. A. I. Saichev and G. M. Zaslavsky, Chaos 7, 753 (1997). 10.1063/1.166272 (Pubitemid 128005624)
15. A. A. Dubkov and B. Spagnolo, Fluct. Noise Lett. 5, L267 (2005). 10.1142/S0219477505002641 (Pubitemid 41124095)
16. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
17. J. Tunaley, J. Stat. Phys. 11, 397 (1974). 10.1007/BF01026731
18. M. Kotulski, J. Stat. Phys. 81, 777 (1995). 10.1007/BF02179257
19. Lévy Processes in Theory and Applications, edited by, O. E. Barndorff-Nielsen, T. Mikosch, and, S. I. Resnick, (Birkhäuser, Boston, 2001).
20. E. Barkai, Chem. Phys. 284, 13 (2002). 10.1016/S0301-0104(02)00533-5
21. V. V. Uchaikin, Phys. Usp. 46, 821 (2003). 10.1070/ PU2003v046n08ABEH001324 (Pubitemid 44384988)
22. T. Srokowski, Physica A 388, 1057 (2009). 10.1016/j.physa.2008.12.059
23. E. Scalas, Physica A 362, 225 (2006). 10.1016/j.physa.2005.11.024 (Pubitemid 43234049)
24. G. Germano, M. Politi, E. Scalas, and R. L. Schilling, Phys. Rev. E 79, 066102 (2009). 10.1103/PhysRevE.79.066102
25. E. W. Montroll and G. H. Weiss, J. Math. Phys. 6, 167 (1965). 10.1063/1.1704269
26. R. Hilfer and L. Anton, Phys. Rev. E 51, R848 (1995). 10.1103/PhysRevE.51.R848
27. M. M. Meerschaert and E. Scalas, Physica A 370, 114 (2006). 10.1016/j.physa.2006.04.034 (Pubitemid 44247364)
28. M. Magdziarz, A. Weron, and K. Weron, Phys. Rev. E 75, 016708 (2007). 10.1103/PhysRevE.75.016708 (Pubitemid 46174720)
29. M. Magdziarz and A. Weron, Phys. Rev. E 75, 056702 (2007). 10.1103/PhysRevE.75.056702 (Pubitemid 47138566)
30. M. Magdziarz, A. Weron, and J. Klafter, Phys. Rev. Lett. 101, 210601 (2008). 10.1103/PhysRevLett.101.210601
31. R. Metzler, E. Barkai, and J. Klafter, Europhys. Lett. 46, 431 (1999). 10.1209/epl/i1999-00279-7
32. S. Jespersen, R. Metzler, and H. C. Fogedby, Phys. Rev. E 59, 2736 (1999). 10.1103/PhysRevE.59.2736
33. E. Scalas, R. Gorenflo, and F. Mainardi, Phys. Rev. E 69, 011107 (2004). 10.1103/PhysRevE.69.011107
34. R. Gorenflo, Chem. Phys. 284, 521 (2002). 10.1016/S0301-0104(02)00714-0
35. M. M. Meerschaert and C. Tadjeran, J. Comput. Appl. Math. 172, 65 (2004). 10.1016/j.cam.2004.01.033 (Pubitemid 39204390)
36. I. M. Sokolov, J. Klafter, and A. Blumen, Phys. Today 55 (11), 48 (2002). 10.1063/1.1535007
37. B. Dybiec, E. Gudowska-Nowak, and P. Hänggi, Phys. Rev. E 73, 046104 (2006). 10.1103/PhysRevE.73.046104
38. S. I. Denisov, W. Horsthemke, and P. Hänggi, Phys. Rev. E 77, 061112 (2008). 10.1103/PhysRevE.77.061112
39. A. Weron and R. Weron, Lect. Notes Phys. 457, 379 (1995). 10.1007/3-540-60188-0-67
40. R. Weron, Stat. Probab. Lett. 28, 165 (1996). 10.1016/0167-7152(95)00113- 1 (Pubitemid 126163062)
41. H. C. Fogedby, Phys. Rev. E 58, 1690 (1998). 10.1103/PhysRevE.58.1690
42. Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008). 10.1103/PhysRevLett.101.058101
43. A. Fuliński, Z. Grzywna, I. Mellor, Z. Siwy, and P. N. R. Usherwood, Phys. Rev. E 58, 919 (1998). 10.1103/PhysRevE.58.919
44. B. Dybiec, J. Stat. Mech. (2009) P08025. 10.1088/1742-5468/2009/08/P08025
45. B. Dybiec and E. Gudowska-Nowak, EPL 88, 10003 (2009). 10.1209/0295-5075/88/10003
46. I. M. Sokolov, Phys. Rev. E 63, 011104 (2000). 10.1103/PhysRevE.63.011104
47. J. M. Sancho, A. M. Lacasta, K. Lindenberg, I. M. Sokolov, and A. H. Romero, Phys. Rev. Lett. 92, 250601 (2004). 10.1103/PhysRevLett.92.250601
48. V. V. Belik and D. Brockmann, New J. Phys. 9, 54 (2007). 10.1088/1367-2630/9/3/054 (Pubitemid 46417521)
49. A. Lubelski and J. Klafter, J. Phys. Chem. B 112, 12740 (2008). 10.1021/jp800242b
50. R. Metzler, V. Tejedor, J. H. Jeon, Y. He, W. H. Deng, S. Burov, E. Barkai, Acta Phys. Pol. B 40, 1315 (2009).
51. I. Bronstein, Y. Israel, E. Kepten, S. Mai, Y. Shav-Tal, E. Barkai, and Y. Garini, Phys. Rev. Lett. 103, 018102 (2009). 10.1103/PhysRevLett.103.018102