Superdiffusion of a random walk driven by an ergodic Markov process with switching

Journal of Physics A: Mathematical and Theoretical

Volumn 40, Issue 22, 2007, Pages 5769-5782

  Fedotov, S ^a   Milstein, G N ^b   Tretyakov, M V ^c  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b URAL FEDERAL UNIVERSITY   (Russian Federation)

^c UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34249307812     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/40/22/001     Document Type: Article

References (33)

1. Babovsky H and Milstein G N 1999 Transport equations with singularity Transp. Theory Stat. Phys. 28 575-95
2. Beran J 1994 Statistics for Long-memory Processes (New York: Chapman and Hall)
3. Bouchaud J-P and Georges A 1990 Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications Phys. Rep. 195 127-293
4. Costa O 1990 Stationary distributions for piecewise-deterministic Markov processes J. Appl. Probab. 27 60-73
5. Davis M 1984 Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models J. R. Stat. Soc. Ser. B 46 353-88
6. Dufour F and Costa O L V 1999 Stability of piecewise-deterministic Markov processes SIAM J. Control Optim. 37 1483-502
7. Dynkin E B 1965 Markov Processes (Berlin: Springer)
8. Fedotov S and Iomin A 2007 Migration and proliferation dichotomy in tumor cell invasion Phys. Rev. Lett. 98 118101
9. Fedotov S and Iomin A 2007 Migration and proliferation dichotomy in tumor cell invasion Phys. Rev. Lett. 98 4 p
10. Gaveau B, Jacobson T, Kac M and Schulman L S 1984 Relativistic extension of the analogy between quantum mechanics and Brownian motion Phys. Rev. Lett. 53 419-22
11. Goychuk I and Hanggi P 2003 Non-Markovian stochastic resonance Phys. Rev. Lett. 91 070601 4 p
12. Goychuk I and Hanggi P 2004 Fractional diffusion modeling of ion channel gating Phys. Rev. E 70 051915
13. Goychuk I and Hanggi P 2004 Fractional diffusion modeling of ion channel gating Phys. Rev. E 70 9 p
14. Goychuk I and Hanggi P 2006 Quantum two-state dynamics driven by stationary non-Markovian discrete noise: exact results Chem. Phys. 324 160-71
15. Grünbaum D 2000 Advection-diffusion equations for internal state-mediated random walks SIAM J. Appl. Math. 61 43-73
16. Ito K and McKean H P 1965 Diffusion Processes and Their Sample Paths (Berlin: Springer)
17. Hille B 1992 Ionic Channels of Excitable Membranes (Sunderland, MA: Sinauer Inc.)
18. Kac M 1974 A stochastic model related to the telegrapher's equation Rocky Mt. J. Math. 4 497-509
19. Khasminskii R Z 1980 Stochastic Stability of Differential Equations (Alphen aan den Rijn: Sijthoff and Noordhoff)
20. McNamara B and Wiesenfeld K 1989 Theory of stochastic resonance Phys. Rev. A 39 4854-69
21. Metzler R and Klafter J 2000 The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys. Rep. 339 1-77
22. Metzler R and Klafter J 2004 The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics J. Phys. A: Math. Gen. 37 R161-208
23. Milstein G N 1972 Interaction of Markov processes Theory Prob. Appl. 17 36-45
24. Milstein G N and Repin Yu M 1969 The action of a Markov process on a system of differential equations Differ. Equ. 5 1371-84
25. Milstein G N and Tretyakov M V 2004 Stochastic Numerics for Mathematical Physics (Berlin: Springer)
26. Montroll E W and Weiss G H 1965 Random walks on lattices: II J. Math. Phys. 6 167-81
27. Othmer H G and Stevens A 1997 Aggregation, blowup, and collapse: the ABC's of taxis in reinforced random walks SIAM J. Appl. Math. 57 1044-81
28. Shlesinger M F, West B and Klafter J 1987 Lévy dynamics of enhanced diffusion: application to turbulence Phys. Rev. Lett. 58 1100-3
29. Shushin A I 2001 Anomalous two-state model for anomalous diffusion Phys. Rev. E 64 051108 12 p
30. West B, Bologna M and Grigolini P 2003 Physics of Fractal Operators (Berlin: Springer)
31. West B J, Grigolini P, Metzler R and Nonnenmacher Th F 1997 Fractional diffusion and Lévy stable processes Phys. Rev. E 55 99-106
32. Zaslavsky G M 2002 Chaos, fractional kinetics, and anomalous transport Phys. Rep. 371 461-580
33. Zumofen G and Klafter J 1993 Scale-invariant motion in intermittent chaotic systems Phys. Rev. E 47 851-63