From Ornstein-Uhlenbeck dynamics to long-memory processes and fractional Brownian motion

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 2, 2009, Pages

  Eliazar, Iddo ^a   Klafter, Joseph ^b,c  

^a HOLON INSTITUTE OF TECHNOLOGY   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

^c UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS;

COLLECTIVE SYSTEMS; FRACTIONAL BROWNIAN MOTIONS; LONG MEMORIES; LONG-MEMORY PROCESS; MOVING AVERAGES; ORNSTEIN-UHLENBECK DYNAMICS; QUENCHED DISORDERS; STATISTICAL VARIABILITIES; TEMPORAL CORRELATIONS; TIME-SCALES;

BROWNIAN MOVEMENT;

EID: 61949257949     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.021115     Document Type: Article

References (40)

1. G. E. Uhlenbeck and L. S. Ornstein, Phys. Rev. 36, 823 (1930). 10.1103/PhysRev.36.823
2. W. T. Coffey, Yu. P. Kalmykov, and J. T. Waldron, The Langevin Equation, 2nd ed. (World Scientific, Singapore, 2004).
3. I. Eliazar and J. Klafter, Proc. Natl. Acad. Sci. U.S.A. 102, 13779 (2005). 10.1073/pnas.0506816102
4. I. Eliazar and J. Klafter, Physica A 360, 227 (2006). 10.1016/j.physa.2005.06.056
5. A. Janicki and A. Weron, Simulation and Chaotic Behavior of Stable Stochastic Processes (Marcel Dekker, New York, 1994).
6. G. Samrodintsky and M. S. Taqqu, Stable Non-Gaussian Random Processes (Chapman and Hall, New York, 1994).
7. H. C. Fogedby, Phys. Rev. E 50, 1657 (1994). 10.1103/PhysRevE.50.1657
8. S. Jespersen, R. Metzler, and H. C. Fogedby, Phys. Rev. E 59, 2736 (1999). 10.1103/PhysRevE.59.2736
9. A. V. Chechkin Chem. Phys. 284, 233 (2002). 10.1016/S0301-0104(02)00551-7
10. A. V. Chechkin J. Klafter, V. Y. Gonchar, R. Metzler, and L. V. Tanatarov, Phys. Rev. E 67, 010102 (R) (2003). 10.1103/PhysRevE.67.010102
11. I. Eliazar and J. Klafter J. Stat. Phys. 111, 739 (2003). 10.1023/A:1022894030773
12. I. Eliazar and J. Klafter, J. Stat. Phys. 119, 165 (2005). 10.1007/s10955-004-2710-9
13. I. Eliazar and J. Klafter, J. Phys. A 40, F307 (2007). 10.1088/1751-8113/40/16/F03
14. M. Magdziarz and A. Weron, Phys. Rev. E 75, 056702 (2007). 10.1103/PhysRevE.75.056702
15. M. Magdziarz, Physica A 387, 123 (2008). 10.1016/j.physa.2007.08.016
16. D. R. Cox, in Statistics: An Appraisal, edited by, H. A. David, and, H. T. David, (Iowa State University Press, Ames, 1984), pp. 55-74.
17. P. Dounkan, G. Oppenheim, and M. S. Taqqu, Theory and Applications of Long-range Dependence, (Birkhauser, Boston, 2003).
18. Processes with Long-range Correlations: Theory and Applications, edited by, G. Rangarajan, and, M. Ding, Lecture Notes in Physics No. 621 (Springer, New York, 2003).
19. E. Iglói and G. Terdik, Electron. J. Probab. 4, 1 (1999).
20. O. E. Barndorff-Nielsen and N. N. Leonenko, Methodol. Comput. Appl. Probab. 7, 335 (2005). 10.1007/s11009-005-4521-0
21. N. N. Leonenko and E. Taufer, Stochastics Dyn. 77, 477 (2005).
22. B. B. Mandelbrot and J. W. Van Ness, SIAM Rev. 10, 422 (1968). 10.1137/1010093
23. P. Embrechts and M. Maejima, Self-similar Processes (Princeton University Press, Princeton, 2002).
24. E. Lutz, Phys. Rev. E 64, 051106 (2001). 10.1103/PhysRevE.64.051106
25. R. Kupferman, J. Stat. Phys. 114, 291 (2004). 10.1023/B:JOSS.0000003113. 22621.f0
26. W. Whitt, An Introduction to Stochastic-process Limits and Their Applications to Queues (Springer, New York, 2002).
27. B. B. Mandelbrot, Int. Econom. Rev. 10, 82 (1969). 10.2307/2525574
28. M. S. Taqqu and J. Levy, in Dependence in Probability and Statistics edited by, E. Eberlein, and, M. S. Taqqu, (Birkhauser, Boston, 1986), pp. 73-89.
29. M. S. Taqqu, W. Willinger, and R. Sherman, Comput. Commun. Rev. 27, 5 (1997). 10.1145/263876.263879
30. N. Enriquez, Stochastic Proc. Appl. 109, 203 (2004). 10.1016/j.spa.2003. 10.008
31. I. Eliazar and J. Klafter, J. Phys. A: Math. Theor. 41, 122001 (2008). 10.1088/1751-8113/41/12/122001
32. R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, Oxford, 2001).
33. J. Bernamont, Ann. Phys. 7, 71 (1937).
34. A. R. Butz, J. Stat. Phys. 4, 199 (1972). 10.1007/BF01008550
35. A. van der Ziel, Adv. Electron. Electron Phys. 49, 225 (1979).
36. P. Brémaud, Mathematical Principles of Signal Processing (Springer, New York, 2002).
37. N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation (Cambridge University Press, Cambridge, 1987).
38. B. B. Mandelbrot and J. R. Wallis, Water Resour. Res. 4, 909 (1968). 10.1029/WR004i005p00909
39. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed. (Springer, New York, 1991).
40. W. Feller, An Introduction to Probability Theory and its Applications, 2nd ed. (Wiley, New York, 1971), Vol. 2.