Continuous Markovian model for Lévy random walks with superdiffusive and superballistic regimes

European Physical Journal B

Volumn 78, Issue 2, 2010, Pages 207-216

  Lubashevsky, I A ^a   Heuer, A ^b   Friedrich, R ^b   Usmanov, R ^c,d  

^a UNIVERSITY OF AIZU   (Japan)

^b UNIVERSITY OF MÜNSTER   (Germany)

^c MIREA RUSSIAN TECHNOLOGICAL UNIVERSITY   (Russian Federation)

^d PROKHOROV GENERAL PHYSICS INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DIVERGENT MOMENTS; GEOMETRIC MEAN; LANGEVIN EQUATION; MARKOVIAN MODEL; POWER-LAW TAIL; RANDOM WALK; SUPERDIFFUSIVE REGIMES; TIME-SCALES; VELOCITY CORRELATIONS;

BALLISTICS; DIFFERENTIAL EQUATIONS; MARKOV PROCESSES; NONLINEAR EQUATIONS;

PROBABILITY DENSITY FUNCTION;

EID: 78650893898     PISSN: 14346028     EISSN: 14346036     Source Type: Journal    
DOI: 10.1140/epjb/e2010-10422-4     Document Type: Article

References (54)

1. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982)
2. J.-P. Bouchaud A. Georges 1990 Phys. Rep. 195 127 1081295 1990PhR...195..127B 10.1016/0370-1573(90)90099-N
3. B.J. West W. Deering 1994 Phys. Rep. 246 1 1994PhR...246....1W 10.1016/0370-1573(94)00055-7
4. Lévy Flights, and Related Topics in Physics, edited by M.F. Shlesinger, G.M. Zaslavsky, U. Frisch (Springer, Berlin, 1995)
5. R. Metzler J. Klafter 2000 Phys. Rep. 339 1 0984.82032 1809268 2000PhR...339....1M 10.1016/S0370-1573(00)00070-3
6. M. Dentz H. Scher D. Holder B. Berkowitz 2008 Phys. Rev. E 78 041110 2008PhRvE..78d1110D 10.1103/PhysRevE.78.041110
7. T. Koren M.A. Lomholt A.V. Chechkin J. Klafter 2007 Phys. Rev. Let. 99 160602 2007PhRvL..99p0602K 10.1103/PhysRevLett.99.160602 (Pubitemid 47613344)
8. T. Koren A.V. Chechkin J. Klafter 2007 Physica A 379 10 2308361 2007PhyA..379...10K 10.1016/j.physa.2006.12.039 (Pubitemid 46453054)
9. M.A. Lomholt T. Ambjörnsson R. Metzler 2005 Phys. Rev. Lett. 95 260603 2005PhRvL..95z0603L 10.1103/PhysRevLett.95.260603 (Pubitemid 43061524)
10. H. Katory S. Schlipf H. Walther 1997 Phys. Rev. Lett. 79 2221 1997PhRvL..79.2221K 10.1103/PhysRevLett.79.2221
11. H.C. Fogedby 1994 Phys. Rev. E 50 1657 1994PhRvE..50.1657F 10.1103/PhysRevE.50.1657
12. A.A. Stanislavsky 2003 Phys. Rev. E 67 021111 1974618 2003PhRvE..67b1111S 10.1103/PhysRevE.67.021111
13. P.D. Ditlevsen 1999 Phys. Rev. E 60 172 1999PhRvE..60..172D 10.1103/PhysRevE.60.172
14. A. Dubkov B. Spagnolo 2005 Fluc. Noise Lett. 5 L267 2165213 10.1142/S0219477505002641 (Pubitemid 41124095)
15. S. Marksteiner K. Ellinger P. Zoller 1996 Phys. Rev. A 53 3409 1996PhRvA..53.3409M 10.1103/PhysRevA.53.3409
16. E. Lutz 2004 Phys. Rev. Lett. 93 190602 2004PhRvL..93s0602L 10.1103/PhysRevLett.93.190602
17. E. Barkai R.J. Silbey 2000 J. Phys. Chem. B 104 3866 10.1021/jp993491m
18. R. Metzler I.M. Sokolov 2002 Europhys. Lett. 58 482 2002EL.....58..482M 10.1209/epl/i2002-00421-1
19. R. Friedrich F. Jenko A. Baule S. Eule 2006 Phys. Rev. Lett. 96 230601 2006PhRvL..96w0601F 10.1103/PhysRevLett.96.230601 (Pubitemid 43877300)
20. H. Affan R. Friedrich S. Eule 2009 Phys. Rev. E 80 011137 2009PhRvE..80a1137A 10.1103/PhysRevE.80.011137
21. C. Tsallis D.J. Bukman 1996 Phys. Rev. E 54 R2197 1996PhRvE..54.2197T 10.1103/PhysRevE.54.R2197
22. A. Schenzle H. Brand 1979 Phys. Rev. A 20 1628 1979PhRvA..20.1628S 10.1103/PhysRevA.20.1628
23. W. Horsthemke, R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry and Biology (Springer-Verlag, Berlin, 1984)
24. H. Konno P.S. Lomdahl 2004 J. Phys. Soc. Jpn 73 573 1056.60100 2004JPSJ...73..573K 10.1143/JPSJ.73.573 (Pubitemid 40767499)
25. H. Konno F. Watanabe 2007 J. Math. Phys. 48 103303 2362792 2007JMP....48j3303K 10.1063/1.2800162
26. S.C. Venkataramani T.M. Antonsen Jr 1996 Physica D 96 66 1194.37147 1414511 10.1016/0167-2789(96)00014-0
27. H. Takayasu A.-H. Sato M. Takayasu 1997 Phys. Rev. Lett. 79 966 0971.82033 1997PhRvL..79..966T 10.1103/PhysRevLett.79.966
28. J.M. Deutsch 1994 Physica A 208 433 1994PhyA..208..433D 10.1016/0378-4371(94)00055-7
29. H. Sakaguchi 2001 J. Phys. Soc. Jpn 70 3247 1091.82503 2001JPSJ...70.3247S 10.1143/JPSJ.70.3247
30. I. Lubashevsky R. Friedrich A. Heuer 2009 Phys. Rev. E 79 011110 2552186 2009PhRvE..79a1110L 10.1103/PhysRevE.79.011110
31. I. Lubashevsky R. Friedrich A. Heuer 2009 Phys. Rev. E 80 031148 2552186 2009PhRvE..80c1148L 10.1103/PhysRevE.80.031148
32. G.M. Zaslavsky 2002 Phys. Rep. 371 461 0999.82053 1937584 2002PhR...371..461Z 10.1016/S0370-1573(02)00331-9
33. L.F. Richardson 1926 Ser. A 110 709
34. M.F. Shlesinger B.J. West J. Klafter 1987 Phys. Rev. Lett. 58 1100 884850 1987PhRvL..58.1100S 10.1103/PhysRevLett.58.1100
35. J.A. Viecelli 1992 Phys. Fluids A 45 8407
36. G. Zimbardo A. Greco P. Veltri 2000 Phys. Plasma 7 1071 2000PhPl....7.1071Z 10.1063/1.873914
37. N.T. Ouellette H. Xu M. Bourgoin E. Bodenschatz 2006 New J. Phys. 8 109 2006NJPh....8..109O 10.1088/1367-2630/8/6/109 (Pubitemid 43938992)
38. S. Pradham Y.S. Mayya B.N. Jagatap 2007 Phys. Rev. E 76 033407 2007PhRvA..76C3407P
39. G.M. Viswanathan E.P. Raposo M.G.E. da Luz 2008 Phys. Life Rev. 5 133 2008PhLRv...5..133V 10.1016/j.plrev.2008.03.002
40. M.J. Plank A. James 2008 J.R. Soc. Interface 5 1077 10.1098/rsif.2008. 0006 (Pubitemid 352020059)
41. C. Hawkes 2009 J. Anim. Ecol. 78 894 10.1111/j.1365-2656.2009.01534.x
42. M.C. Santos E.P. Raposo G.M. Viswanathan M.G.E. da Luz 2004 Europhys. Lett. 67 734 2004EL.....67..734S 10.1209/epl/i2004-10114-9 (Pubitemid 39196514)
43. A. James M.J. Plank R. Brown 2008 Phys. Rev. E 78 051128 2008PhRvE..78e1128J 10.1103/PhysRevE.78.051128
44. M.C. Mariani Y. Liu 2007 Physica A 377 590 2007PhyA..377..590M 10.1016/j.physa.2006.11.066 (Pubitemid 46199103)
45. A. Figueiredo I. Gleria R. Matsushita S. Da Silva 2003 Physics A 323 601 1072.91601 1982267 2003PhyA..323..601F 10.1016/S0378-4371(03)00029-3
46. R. Matsushita P. Rathie S. Da Silva 2003 Physica A 326 544 1027.60040 2003564 2003PhyA..326..544M 10.1016/S0378-4371(03)00363-7
47. M.C. Mariani J.B. Libbin V.K. Mani M.P.B. Varela C.A. Erickson D.J. Valles-Rosales 2008 Physica A 387 1273 2008PhyA..387.1273M 10.1016/j.physa.2007. 10.064 (Pubitemid 350213282)
48. A. Röler 2005 Proc. Appl. Math. Mech. 5 817 10.1002/pamm.200510380
49. A. Röler 2009 SIAM J. Numer. Anal. 47 1713 1193.65006 2505871 10.1137/060673308
50. A. Papoulis, Probability, Random Variables, and Stochastic Process (McGraw-Hill, New York, 1991)
51. G. Bel I. Nemenman 2009 New J. Phys. 11 083009 2009NJPh...11h3009B 10.1088/1367-2630/11/8/083009
52. W. Deng E. Barkai 2009 Phys. Rev. E 79 011112 2552187 2009PhRvE..79a1112D 10.1103/PhysRevE.79.011112
53. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006)
54. H. Konno, private communication