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

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Iddo Eliazar1 and Joseph Klafter2

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[1]
Uhlenbeck G E and Ornstein L S 1930 Phys. Rev. 36 823
CrossRef 
[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
CrossRef 
[4]
Embrechts P and Maejima M 2002 Selfsimilar Processes (Princeton, NJ: Princeton University Press)

[5]
Lutz E 2001 Phys. Rev. E 64 051106
CrossRef 
[6]
Kupferman R 2004 J. Stat. Phys. 114 291
CrossRef 
[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
CrossRef 
[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
CrossRef 
[11]
Enriquez N 2004 Stochast. Proc. Appl. 109 203
CrossRef 
[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
CrossRef 
[15]
Eliazar I and Klafter J 2005 Proc. Natl Acad. Sci. 102 13779
CrossRef  PubMed 
[16]
Eliazar I and Klafter J 2006 Physica A 360 227
CrossRef 
[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
CrossRef 
[20]
Jespersen S, Metzler R and Fogedby H C 1999 Phys. Rev. E 59 2736
CrossRef 
[21]
Garbaczewski P and Olkiewicz R 2000 J. Math. Phys. 41 6843
CrossRef 
[22]
Barndorff-Nielsen O E and Shephard N 2001 J. R. Stat. Soc. B 63 167
CrossRef 
[23]
Chechkin A V et al 2002 Chem. Phys. 284 233
CrossRef 
[24]
Chechkin A V et al 2003 Phys. Rev. E 67 010102
CrossRef 
[25]
Eliazar I and Klafter J 2003 J. Stat. Phys. 111 739
CrossRef 
[26]
Eliazar I and Klafter J 2007 J. Phys. A: Math. Theor. 40 F307
IOPscience 
[27]
Magdziarz M and Weron A 2007 Phys. Rev. E 75 056702
CrossRef 
[28]
Magdziarz M 2008 Physica A 387 123
CrossRef 
[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
CrossRef 
[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)
CrossRef 
[36]
Mandelbrot B B and Wallis J R 1968 Water Resour. Res. 4 909
CrossRef 
[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)

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