Multidimensional Lévy walk and its scaling limits

Journal of Physics A: Mathematical and Theoretical

Volumn 45, Issue 38, 2012, Pages

  Teuerle, Marek ^a   Z̊ebrowski, Piotr ^b   Magdziarz, Marcin ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b UNIVERSITY OF WROC AW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84866360565     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/45/38/385002     Document Type: Article

References (54)

1. Scher H and Montroll E W 1975 Phys. Rev. B 12 2455
2. Scher H, Metzler R, Margolin G, Klafter J and Berkowitz B 2002 Geophys. Res. Lett. 29 1061
3. Nelson J and Chandler R E 2004 Coord. Chem. Rev. 248 1181
4. Bologna M, Grigolini P and Riccardi J 1999 Phys. Rev. E 60 6435
5. Ott A, Bouchaud J-P, Langevin D and Urbach W 1994 Phys. Rev. Lett. 65 2201
6. Barthelemy P, Bertolotti J and Wiersma D S 2008 Nature 453 495
7. Zumofen G, Klafter J and Blumen A 1990 Chem. Phys. 146 433
8. Klafter J, Blumen A, Zumofen G and Shlesinger M F 1990 Physica A 168 637
9. Becker-Kern P, Meerschaert M M and Scheffler H P 2004 Ann. Probab. 32 730
10. Jurlewicz A, Kern P, Meerschaert M M and Scheffler H P 2011 Comput. Math. Appl. at press (doi: 10.1016/j.camwa.2011.10.010)
11. Henry B I and Straka P 2011 Stochastic Process. Appl. 121 324
12. Metzler R and Klafter J 2000 Phys. Rep. 339 1
13. Sokolov I M 2000 Phys. Rev. E 63 011104
14. Brockmann D and Hufnagel L 2007 Phys. Rev. Lett. 98 178301
15. Escande F and Sattin F 2007 Phys. Rev. Lett. 99 185005
16. Klafter J, Koren T and Magdziarz M 2007 Phys. Rev. E 76 031129
17. Magdziarz M and Weron A 2007 Phys. Rev. E 75 056702
18. Shlesinger M F and Klafter J 1985 Phys. Rev. Lett. 54 2551
19. Zumofen G, Klafter J and Blumen A 1993 Phys. Rev. E 47 2183
20. Brockmann D, Hufnagel L and Geisel T 2006 Nature 439 462
21. Gonzales M C, Hidalgo C A and Barabasi A L 2008 Nature 453 779
22. Brockmann D 2010 Human Mobility and Spatial Disease Dynamics (Reviews of Nonlinear Dynamics and Complexity vol 2) ed H Shuster (Weinheim: Wiley)
23. Janssen H K, Oerding K, van Wijland F and Hilhorst H J 1999 Eur. Phys. J. B 7 137
24. Dybiec B 2008 Physica A 387 4863
25. Bell W J 1999 Searching Behaviour (London: Chapman and Hall)
26. Berg H C 1983 Random Walks in Biology (Princeton, NJ: Princeton University Press)
27. Ramos-Fernandez G, Mateos J L, Miramontes O, Cocho G, Larralde F and Ayala-Orozco B 2004 Behav. Ecol. Sociobiol. 55 223
28. Edwards A et al 2007 Nature 449 1044
29. Reynolds A M, Smith A D, Menzel R, Greggers U, Reynolds D R and Riley J R Ecology 88 1955
30. Buchanan M 2008 Nature 453 714
31. Sims D W et al 2008 Nature 451 1098
32. Viswanathan G M, Buldyrev S V, Havlin S, da Luz M G E, Raposo E P and Stanley H E 1999 Nature 401 901
33. Janicki A and Weron A 1994 Simulation and Chaotic Behavior of α-Stable Stochastic Processes (New York: Dekker)
34. Magdziarz M, Weron A and Weron K 2007 Phys. Rev. E 75 016708
35. Meerschaert M M, Benson D, Scheffler H P and Baeumer B 2002 Phys. Rev. E 65 041103
36. Magdziarz M, Szczotka W and ebrowski P 2012 J. Stat. Phys. 147 74
37. Teuerle M, ebrowski P and Magdziarz M 2012 Acta Phys. Pol. B 43 1111
38. Samorodnitsky G and Taqqu M 1994 Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (New York: Chapman and Hall)
39. Fogedby H C 1994 Phys. Rev. E 50 1657
40. Meerschaert M M and Sikorskii A 2012 Stochastic Models for Fractional Calculus (Berlin: de Gruyter & Co)
41. Schumer R, Benson D, Meerschaert M M and Baeumer B 2003 Water Resources Res. 39 1022
42. Zhang Y, Benson D, Meerschaert M M, LaBolle E M and Scheffler H P 2006 Phys. Rev. E 74 026706
43. Teuerle M and Jurlewicz A 2009 Acta Phys. Pol. B 40 1001
44. Codling E A and Hill N A 2005 J. Theor. Biol. 233 573
45. Codling E A, Hill N A, Pitchford J W and Simpson S D 2004 Mar. Ecol. Prog. Ser. 279 215
46. Bartumeus F, Catalan J, Viswanathan G M, Raposo E P and da Luz M G E 2008 J. Theor. Biol. 252 43
47. Jammalamadaka S R and SenGupta A 2001 Topics in Circular Statistics (New York: World Scientific)
48. Fisher N I Statistical Analysis of Circular Data (Cambridge: Cambridge University Press)
49. Nolan J P, Panorska A K and McCulloch J H 2001 Math. Comput. Model. 34 1113
50. Gnedenko B V and Kolmogorov A N 1954 Limit Distributions for Sums of Independent Random Variables (Boston, MA: Addison-Wesley)
51. Meerschaert M M and Scheffler H P 2004 J. Appl. Probab. 41 623
52. Meerschaert M M and Scheffler H P 2001 Limit Distributions for Sums of Independent Random Vectors (New York: Wiley Interscience)
53. Whitt W 2002 Stochastic-Process Limits (New York: Springer)
54. Billingsley P 1968 Convergence of Probability Measures (New York: Wiley)