Publication: The path integral formulation of fractional Brownian motion for the general Hurst exponent
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2008-07-18
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Institute of Physics
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Abstract
In 1995, Sebastian (1995 J. Phys. A: Math. Gen. 28 4305) gave a path integral computation of the propagator of subdiffusive fractional Brownian motion (fBm), i.e. fBm with a Hurst or self-similarity exponent H ∈ (0, 1/2). The extension of Sebastian's calculation to superdiffusion, H ∈ (1/2, 1], becomes however quite involved due to the appearance of additional boundary conditions on fractional derivatives of the path. In this communication, we address the construction of the path integral representation in a different fashion, which allows us to treat both subdiffusion and superdiffusion on an equal footing. The derivation of the propagator of fBm for the general Hurst exponent is then performed in a neat and unified way.
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5 pages, no figures.-- PACS nrs.: 05.40.-a, 02.50.Ey, 05.10.Gg.-- ArXiv preprint available at: http://arxiv.org/abs/0805.1170
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[PACS] Fluctuation phenomena, random processes, noise, and Brownian motion, [PACS] Stochastic processes, [PACS] Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
Bibliographic citation
J. Phys. A: Math. Theor. 41, 282002 (2008)