Random walk model with waiting times depending on the preceding jump length

Journal of Statistical Physics

Volumn 123, Issue 4, 2006, Pages 871-881

  Zaburdaev, Vasily Yu ^a  

^a MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

Author keywords

Continuous time random walk model; Coupled transition kernel; Fractional derivatives; Green's function; Levy flights

Indexed keywords

EID: 33747654448     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9104-0     Document Type: Article

References (26)

1. R. Metzler and J. Klafter, The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339(1):1-77 (2000).
2. R. Metzler and J. Klafter, The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A 37:R161-R208 (2004).
3. E. W. Montroll and M. F. Schlesinger, Nonequilibrium phenomena II: From stochastic to hydrodynamics, In J. Leibowitz and E. W. Montroll, eds. Studies in Statistical Mechanics Vol. 11, (North-Holland, Amsterdam, 1984), pp. 1-122.
4. V. V. Uchaikin, Self-similar anomalous diffusion and Levy-stable laws. Physics-Uspekhi 46:821-849 (2003).
5. I. Podlubny, Fractional Differential Equations, (Academic Press, San Diego, 1999), p. 1.
6. I. M. Sokolov, A. V. Chechkin, and J. Klafter, Fractional diffusion equation for a power-law-truncated Levy process. Physica A 336:245-251 (2004).
7. G. Zumofen and J. Klafter, Scale-invariant motion in intermittent chaotic systems. Phys. Rev. E 47(2):851-863 (1993), and references therein.
8. M. F. Shlesinger, J. Klafter, and Y. M. Wong, Random walks with infinite spatial and temporal moments. J. Stat. Phys. 27:499-512 (1982).
9. J. Masoliver, K. Lindenberg, and B. I. West, First-passage times for non-Markovian processes: Correlated impacts on a free process. Phys. Rev. A 34: 1481-1494 (1986);
10. First-passage times for non-Markovian processes: Correlated impacts on bound processes. Phys. Rev. A 34:2351-2363 (1986).
11. G. H. Weiss, J. Masoliver, K. Lindenberg, and B. J. West, First-passage times for non-Markovian processes: Multivalued noise. Phys. Rev. A 36:1435-1439 (1987).
12. J. Klafter, A. Blumen, and M. F. Shlesinger, A stochastic pathway to anomalous diffusion. Phys. Rev. A 35:3081-3085 (1987).
13. V. Yu. Zaburdaev and K. V. Chukbar, Enhanced superdiffusion and finite velocity of Levy flights. JETP 94:252-259 (2002).
14. E. Barkai, CTRW pathways to the fractional diffusion equation. Chem. Phys. 284:13-27 (2002).
15. M. M. Meerschaert, D. A. Benson, H-P. Scheffler, and P. Becker-Kern, Governing equations and solutions of anomalous random walk limits. Phys. Rev. E 66: 060102(R) (2002).
16. I. M. Sokolov and R. Metzler, Towards deterministic equations for Levy walks: The fractional material derivative. Phys. Rev. E 67: 010101(R) (2003).
17. K. V. Chukbar and V. Yu. Zaburdaev, Comment on "Towards deterministic equations for Levy walks: The fractional material derivative". Phys. Rev. E 68: 033101 (2003).
18. S. A. Trigger, G. J. F. van Heijst, and P. P. J. M. Schram, Mean-squared displacements for normal and anomalous diffusion of grains. J. Phys. Conf. Ser. 11:37-46 (2005).
19. K. V. Chukbar, Stochastic transfer and fractal derivatives. JETP 81:1025-1029 (1995).
20. V. Yu. Zaburdaev and K. V. Chukbar, Memory effects in stochastic transport. JETP Lett. 77:551-555 (2003).
21. E. Barkai, Aging in subdiffusion generated by a determenistic dynamical system. Phys. Rev. Lett. 90:104101 (2003).
22. I. M. Sokolov, A. Blumen, J. Klafter, Dynamics of annealed systems under external fields: CTRW and the fractional Fokker-Planck equations. Europhys. Lett. 56:175-180 (2001).
23. J. Klafter and I. Sokolov, Anomalous diffusion spreads its wings. Physics World, August 2005:29-32 (2005).
24. G. Ramos-Fernández, J. L. Mateos, O. Miramontes, et al., Levy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi). Behav. Ecol. Sociob. 55:223-230 (2004).
25. L. Schimansky-Geier, U. Erdmann, and N. Komin, Advantages of hopping on a zig-zag course. Physica A 351:51-59 (2005).
26. A. Ordemann, G. Balazsi, and F. Moss, Pattern formation and stochastic motion of the Zooplankton Daphnia in a light field. Physica A 325:260-266 (2003).