When does fractional Brownian motion not behave as a continuous function with bounded variation?

Azmoodeh, Ehsan; Tikanmäki, Heikki; Valkeila, Esko

doi:10.48550/arxiv.1004.1071

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Fractional Langevin Of Distributed Order1

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2011

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“…However, theory based on abstract integrals will encounter difficulty in physical interpretations in certain applications. Since our subsequent discussion deals with applications involving 1/2 < H < 1, it is possible to consider the integrals with respect to fractional Brownian motion as the pathwise Riemann-Stieltjes integrals (see for example [41] and references given there). In this way we can handle such integrals in a similar manner as ordinary integrals.…”

Section: Fractional Langevin Of Distributed Ordermentioning

confidence: 99%

Fractional Langevin equations of distributed order

Eab

Lim

2011

Phys. Rev. E

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Distributed-order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be used to model the kinetics of retarding subdiffusion whose scaling exponent decreases with time and the strongly anomalous ultraslow diffusion with mean square displacement which varies asymptotically as a power of logarithm of time.

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Section: Fractional Langevin Of Distributed Ordermentioning

confidence: 99%