Iddo Eliazar and Joseph Klafter 2008 J. Phys. A: Math. Theor. 41 122001 doi:10.1088/1751-8113/41/12/122001
Markov-breaking and the emergence of long memory in Ornstein–Uhlenbeck systems
FREE ARTICLEIddo Eliazar1 and Joseph Klafter2
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We consider a complex system composed of many non-identical parts where (i) the dynamics of each part are Ornstein–Uhlenbeck; (ii) all parts are driven by a common external Lévy noise; and (iii) the system's collective output is the averaged aggregate of the outputs of its parts. Whereas the dynamics on the 'microscopic' parts-level are Markov, the dynamics on the 'macroscopic' system-level are not Markov—and may display a long memory. Moreover, the universal temporal scaling limit of the system's output, in the presence of long memory, is fractional Brownian motion. The model presented is analytically tractable, and gives closed-form quantitative characterizations of both the Markov-breaking phenomenon and the emergence of long memory.
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Issue 12 (28 March 2008)
Received 24 January 2008, in final form 15 February 2008
Published 10 March 2008
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Markov-breaking and the emergence of long memory in Ornstein–Uhlenbeck systems
Iddo Eliazar and Joseph Klafter 2008 J. Phys. A: Math. Theor. 41 122001
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