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Fractional Diffusion in Gaussian Noisy Environment
dc.contributor.author | Hu, Guannan | |
dc.contributor.author | Hu, Yaozhong | |
dc.date.accessioned | 2022-09-12T21:02:49Z | |
dc.date.available | 2022-09-12T21:02:49Z | |
dc.date.issued | 2015-03-31 | |
dc.identifier.citation | Hu, G.; Hu, Y. Fractional Diffusion in Gaussian Noisy Environment. Mathematics 2015, 3, 131-152. https://doi.org/10.3390/math3020131 | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/33447 | |
dc.description.abstract | We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: D(α)tu(t,x)=Bu+u⋅W˙H, where D(α)t is the Caputo fractional derivative of order α∈(0,1) with respect to the time variable t, B is a second order elliptic operator with respect to the space variable x∈Rd and W˙H a time homogeneous fractional Gaussian noise of Hurst parameter H=(H1,⋯,Hd). We obtain conditions satisfied by α and H, so that the square integrable solution u exists uniquely. | en_US |
dc.publisher | MDPI | en_US |
dc.rights | Copyright 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license. | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | en_US |
dc.subject | Fractional derivative | en_US |
dc.subject | Fractional order stochastic heat equation | en_US |
dc.subject | Mild solution | en_US |
dc.subject | Time homogeneous fractional Gaussian noise | en_US |
dc.subject | Stochastic integral of the Itô type | en_US |
dc.subject | Multiple integral of the Itô type | en_US |
dc.subject | Chaos expansion | en_US |
dc.subject | Fox’s H-function | en_US |
dc.subject | Green’s functions | en_US |
dc.title | Fractional Diffusion in Gaussian Noisy Environment | en_US |
dc.type | Article | en_US |
kusw.kuauthor | Hu, Guannan | |
kusw.kuauthor | Hu, Yaozhong | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.3390/math3020131 | en_US |
kusw.oaversion | Scholarly/refereed, publisher version | en_US |
kusw.oapolicy | This item meets KU Open Access policy criteria. | en_US |
dc.rights.accessrights | openAccess | en_US |