A DYNAMICAL APPROACH TO FRACTIONAL BROWNIAN MOTION
Keyword(s):
Herein we develop a dynamical foundation for fractional Brownian motion. A clear relation is established between the asymptotic behavior of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is applicable, we establish a connection between diffusion (either standard or anomalous) and the dynamical indicator known as the Hurst coefficient. We argue on the basis of numerical simulations that although we have been able to prove scaling only for "Gaussian" processes, our conclusions may well apply to a wider class of systems. On the other hand, systems exist for which scaling might not hold, so we speculate on the possible consequences of the various relations derived in the paper on such systems.
2010 ◽
Vol 20
(09)
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pp. 2761-2782
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2020 ◽
Vol 1645
◽
pp. 012004
Keyword(s):
2015 ◽
Vol 36
◽
pp. 1560001
2012 ◽
Vol 7
(3)
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2004 ◽
Vol 17
(2)
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pp. 309-325
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2011 ◽
Vol 16
(4)
◽
pp. 435-452
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