Lévy ratchet in a weak noise limit: Theory and simulation

European Physical Journal: Special Topics

Volumn 191, Issue 1, 2011, Pages 223-237

  Pavlyukevich, I ^a   Dybiec, B ^b   Chechkin, A V ^c,d   Sokolov, I M ^e  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^b JAGIELLONIAN UNIVERSITY   (Poland)

^c TEL AVIV UNIVERSITY   (Israel)

^d KHARKOV INSTITUTE OF PHYSICS AND TECHNOLOGY   (Ukraine)

^e HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79952036125     PISSN: 19516355     EISSN: 19516401     Source Type: Journal    
DOI: 10.1140/epjst/e2010-01352-6     Document Type: Article

References (63)

1. P. P. Lévy, Théorie de l'addition des variables aléatoires (Gauthier-Villars, Paris, 1937).
2. B. Mandelbrot, in The Fractal Geometry of Nature, edited by W. H. Freeman (New York, 1983).
3. W. Feller, An introduction to probability theory and its applications: volume II (John Wiley & Sons, 1971).
4. B. V. Gnedenko, A. N. Kolmogorov, Limit distributions for sums of independent random variables (Addison-Wesley Publishing Company, Cambridge, Mass., 1954).
5. G. Samorodnitsky, M. S. Taqqu, Stable non-Gaussian random processes (Chapman & Hall/CRC, 1994).
6. M. F. Shlesinger, G. M. Zaslavsky, J. Klafter, Nature 363, 31 (1993).
7. J. Klafter, M. F. Shlesinger, G. Zumofen, Phys. Today 49, 33 (1996).
8. T. H. Solomon, E. R. Weeks, H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993).
9. D. del Castillo-Negrete, Phys. Fluids 10, 576 (1998).
10. A. V. Chechkin, V. Yu. Gonchar, M. Szydłowski, Phys. Plasmas 9, 78 (2002).
11. V. Yu. Gonchar, A. V. Chechkin, E. L. Sorokovoi, V. V. Chechkin, E. D. Volkov, Plasma Phys. Rep. 29, 380 (2003).
12. T. Mizuuchi, V. V. Chechkin, K. Ohashi, E. L. Sorokovoy, A. V. Chechkin, V. Yu. Gonchar, K. Takahashi, S. Kobayashi, H. OkadaK. Nagasaki, S. Yamamoto, F. Sano, K. Kondo, N. Nishino, H. Kawazome, H. Shidara, S. Kaneko, Y. Fukagawa, Y. Morita, S. Nakazawa, S. Nishio, S. Tsuboi, M. Yamada, J. Nucl. Mater. 337, 332 (2005).
13. D. del Castillo-Negrete, B. A. Carreras, V. E. Lynch, Phys. Rev. Lett. 94, 065003 (2005).
14. H. Katori, S. Schlipf, H. Walther, Phys. Rev. Lett. 79, 2221 (1997).
15. A. Carati, L. Galgani, B. Pozzi, Phys. Rev. Lett. 90, 010601 (2003).
16. C.-K. Peng, J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley, A. L. Goldberger, Phys. Rev. Lett. 70, 1343 (1993).
17. R. Segev, M. Benveniste, E. Hulata, N. Cohen, A. Palevski, E. Kapon, Y. Shapira, E. Ben-Jacob, Phys. Rev. Lett. 88, 118102 (2002).
18. M. A. Lomholt, T. Ambjörnsson, R. Metzler, Phys. Rev. Lett. 95, 260603 (2005).
19. G. M. Viswanathan, V. Afanasyev, S. V. Buldyrev, E. J. Murphey, P. A. Prince, H. E. Stanley, Nature 381, 413 (1996).
20. O. Sotolongo-Costa, J. C. Antoranz, A. Posadas, F. Vidal, A. Vázquez, Geophys. Res. Lett. 27, 1965 (2000).
21. P. D. Ditlevsen, Geophys. Res. Lett. 26, 1441 (1999).
22. S. A. Kassam, Signal Detection in Non-Gaussian Noise (Springer, 1988).
23. E. J. Wegman, J. B. Thomas, S. C. Schwartz (eds.), Topics in Non-Gaussian Signal Processing (Springer-Verlag, 1988).
24. C. L. Nikias, M. Shao, Signal processing with alpha-stable distributions and applications (Wiley-Interscience, New York, NY, USA, 1995).
25. R. N. Mantegna, H. E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, 1999).
26. J.-P. Bouchaud, M. Potters, Theory of Financial Risks: From Statistical Physics to Risk Management (Cambridge University Press, 2000).
27. R. E. Gomory, B. B. Mandelbrot, Fractals and Scaling In Finance: Discontinuity, Concentration, Risk (Springer, 1997).
28. D. Brockmann, L. Hufnagel, T. Geisel, Nature 439, 462 (2006).
29. P. Barthelemy, J. Bertolotti, D. S. Wiersma, Nature 453, 495 (2008).
30. N. Mercadier, W. Guerin, M. Chevrollier, R. Kaiser, Nat. Phys. 5, 602 (2009).
31. S. Jespersen, R. Metzler, H. C. Fogedby, Phys. Rev. E 59, 2736 (1999).
32. A. V. Chechkin, V. Yu. Gonchar, J. Exper. Theor. Phys. 91, 635 (2000).
33. A. V. Chechkin, V. Yu. Gonchar, J. Klafter, R. Metzler, L. V. Tanatarov, Chem. Phys. 284, 233 (2002).
34. G. Samorodnitsky, M. Grigoriu, Stoch. Proc. Appl. 105, 69 (2003).
35. G. Samorodnitsky, M. Grigoriu, Theor. Math. Phys. 150, 332 (2007).
36. A. Dubkov, B. Spagnolo, Acta Phys. Polon. B 38, 1745 (2007).
37. A. V. Chechkin, J. Klafter, V. Yu. Gonchar, R. Metzler, L. V. Tanatarov, Phys. Rev. E 67, 010102(R) (2003).
38. A. V. Chechkin, V. Yu. Gonchar, J. Klafter, R. Metzler, L. V. Tanatarov, J. Stat. Phys. 115, 1505 (2004).
39. O. Ditlevsen, Prob. Eng. Mech. 19, 385 (2004).
40. B. Dybiec, I. M. Sokolov, A. V. Chechkin, J. Stat. Mech.: Theory Exp., P07008 (2010).
41. P. D. Ditlevsen, Phys. Rev. E 60, 172 (1999).
42. A. V. Chechkin, V. Yu. Gonchar, J. Klafter, R. Metzler, Europhys. Lett. 72, 348 (2005).
43. A. Chechkin, O. Sliusarenko, R. Metzler, J. Klafter, Phys. Rev. E 75, 041101 (2007).
44. B. Dybiec, E. Gudowska-Nowak, P. Hänggi, Phys. Rev. E 75, 021109 (2007).
45. P. Imkeller, I. Pavlyukevich, J. Phys. A: Math. Gen. 39, L237 (2006).
46. P. Imkeller, I. Pavlyukevich, Stoch. Proc. Appl. 116, 611 (2006).
47. P. Imkeller, I. Pavlyukevich, ESAIM: Prob. Stat. 12, 412 (2008).
48. H. Szu, R. Hartley, Phys. Lett. A 122, 157 (1987).
49. I. Pavlyukevich. J. Phys. A: Math. Theor. 40, 12299 (2007).
50. I. Pavlyukevich, J. Comp. Phys. 226, 1830 (2007).
51. D. del Castillo-Negrete, V. Yu. Gonchar, A. V. Chechkin, Physica A 387, 6693 (2008).
52. B. Dybiec, Phys. Rev. E 78, 061120 (2008).
53. B. Dybiec, E. Gudowska-Nowak, I. M. Sokolov, Phys. Rev. E 76, 041122 (2007).
54. B. Dybiec, E. Gudowska-Nowak, New J. Phys. 9, 452 (2007).
55. P. Reimann, Phys. Rep. 361, 57 (2002).
56. B. Dybiec, E. Gudowska-Nowak, I. M. Sokolov, Phys. Rev. E 78, 011117 (2008).
57. M. Vlad, F. Spineanu, S. Benkadda, Phys. Rev. Lett. 96, 085001 (2006).
58. R. Phillips, S. R. Quake, Phys. Today 59, 38 (2006).
59. V. V. Uchaikin, V. M. Zolotarev, Chance and Stability. Stable Distributions and Their Applications (Modern Probability and Statistics. VSP, 1999).
60. A. Janicki, A. Weron, Simulation, Chaotic Behaviour of α-Stable Stochastic Processes, Vol. 178 of Pure and Applied Mathematics (Marcel Dekker, Inc., 1994).
61. A. Janicki, Numerical and Statistical Approximation of Stochastic Differential Equations with non-Gaussian Measures (Hugo Steinhaus Centre for Stochastic Methods, Wrocław, 1996).
62. B. Dybiec, E. Gudowska-Nowak, Fluc. Noise Lett. 4, L273 (2004).
63. B. Dybiec, E. Gudowska-Nowak, P. Hänggi, Phys. Rev. E 73, 046104 (2006).