Markov-breaking and the emergence of long memory in Ornstein-Uhlenbeck systems

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 12, 2008, Pages

  Eliazar, Iddo ^a   Klafter, Joseph ^b  

^a HOLON INSTITUTE OF TECHNOLOGY   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 41149175627     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/12/122001     Document Type: Article

References (38)

1. Uhlenbeck G E and Ornstein L S 1930 Phys. Rev. 36 823
2. Coffey W T, Kalmykov Yu P and Waldron J T 2004 The Langevin Equation 2nd edn (Singapore: World Scientific)
3. Mandelbrot B B and Van Ness J W 1968 SIAM Rev. 10 422
4. Embrechts P and Maejima M 2002 Selfsimilar Processes (Princeton, NJ: Princeton University Press)
5. Lutz E 2001 Phys. Rev. E 64 051106
6. Kupferman R 2004 J. Stat. Phys. 114 291
7. Whitt W 2002 An Introduction to Stochastic-process Limits and their Applications to Queues (New York: Springer)
8. Mandelbrot B B 1969 Int. Econ. Rev. 10 82
9. Taqqu M S and Levy J 1986 Using renewal processes to generate long-range dependence and high variability Dependence in Probability and Statistics ed E Eberlein and M S Taqqu (Boston, MA: Birkhauser) pp 73-89
10. Taqqu M S, Willinger W and Sherman R 1997 Comput. Commun. Rev. 27 5
11. Enriquez N 2004 Stochast. Proc. Appl. 109 203
12. Leonenko N N and Taufer E 2005 Stochastics 77 477
13. Hurst H E 1954 Proc. Inst. Civil Eng. 3 1
14. Eliazar I and Klafter J 2005 J. Stat. Phys. 119 165
15. Eliazar I and Klafter J 2005 Proc. Natl Acad. Sci. 102 13779
16. Eliazar I and Klafter J 2006 Physica A 360 227
17. Samrodintsky G and Taqqu M S 1994 Stable Non-Gaussian Random Processes (New York: Chapman and Hall)
18. Janicki A and Weron A 1994 Simulation and Chaotic Behavior of Stable Stochastic Processes (New York: Dekker)
19. Fogedby H C 1994 Phys. Rev. E 50 1657
20. Jespersen S, Metzler R and Fogedby H C 1999 Phys. Rev. E 59 2736
21. Garbaczewski P and Olkiewicz R 2000 J. Math. Phys. 41 6843
22. Barndorff-Nielsen O E and Shephard N 2001 J. R. Stat. Soc. B 63 167
23. Chechkin A V et al 2002 Chem. Phys. 284 233
24. Chechkin A V et al 2003 Phys. Rev. E 67 010102
25. Eliazar I and Klafter J 2003 J. Stat. Phys. 111 739
26. Eliazar I and Klafter J 2007 J. Phys. A: Math. Theor. 40 F307
27. Magdziarz M and Weron A 2007 Phys. Rev. E 75 056702
28. Magdziarz M 2008 Physica A 387 123
29. Iglói E and Terdik G 1999 Electron. J. Probab. 4 1
30. Barndorff-Nielsen O E and Leonenko N N 2005 Methodol. Comput. Appl. Probab. 7 335
31. Zwanzig R 2001 Nonequilibrium Statistical Mechanics (Oxford: Oxford University Press)
32. Eliazar I and Klafter J From Ornstein-Uhlenbeck dynamics to long-memory processes and fractional Brownian motion (in preparation)
33. Cox D R 1984 Long-range dependence: a review Statistics: An Appraisal ed H A David and H T David (Ames, IA: Iowa State University Press) pp 55-74
34. Dounkan P, Oppenheim G and Taqqu M S (ed) 2003 Theory and Applications of Long-range Dependence (Boston, MA: Birkhauser)
35. Rangarajan G and Ding M (ed) 2003 Processes with Long-range correlations: Theory and Applications (Lecture Notes in Physics vol 621) (New York: Springer)
36. Mandelbrot B B and Wallis J R 1968 Water Resour. Res. 4 909
37. Bingham N H, Goldie C M and Teugels J L 1987 Regular Variation (Cambridge: Cambridge University Press)
38. Feller W 1971 An Introduction to Probability Theory and Its Applications vol II 2nd edn (New York: Wiley)