Garra, R, Issoglio, E orcid.org/0000-0003-3035-2712 and Taverna, GS (2020) Fractional Brownian motions ruled by nonlinear equations. Applied Mathematics Letters, 102. 106160. ISSN 0893-9659
Abstract
In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional differential equation involving fractional Riemann–Liouville time-derivative. Our main contribution is to highlight the link between these generalised equations and fractional Brownian motion (fBm). In particular, we investigate the governing equation of fBm and show that its diffusion coefficient must satisfy an additive evolutive fractional equation. We derive in a similar way the governing equation of the iterated fractional Brownian motion.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Elsevier Ltd. All rights reserved. This is an author produced version of an article published in Applied Mathematics Letters. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Fractional Brownian motions; Iterated fractional Brownian motions; Fractional integrals and derivatives; Nonlinear fractional equations; Time-dependent diffusion coefficient |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Dec 2019 12:42 |
Last Modified: | 29 Nov 2020 01:39 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aml.2019.106160 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:154173 |