On the relation between the fractional Brownian motion and the fractional derivatives

Bibliographic Details
Main Author: Ortigueira, M.D.
Publication Date: 2008
Other Authors: Batista, A. G.
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10362/2416
Summary: Physics Letters A, vol. 372; Issue 7
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spelling On the relation between the fractional Brownian motion and the fractional derivativesForward and backward fractional derivativesGeneralised Cauchy derivativeLiouville derivativeDifferintegrationCentral fractional derivativesFractional stochastic processFractional Brownian motionPhysics Letters A, vol. 372; Issue 7The definition and simulation of fractional Brownian motion are considered from the point of view of a set of coherent fractional derivative definitions. To do it, two sets of fractional derivatives are considered: (a) the forward and backward and (b) the central derivatives, together with two representations: generalised difference and integral. It is shown that for these derivatives the corresponding autocorrelation functions have the same representations. The obtained results are used to define a fractional noise and, from it, the fractional Brownian motion. This is studied. The simulation problem is also considered.Elsevier B.V.RUNOrtigueira, M.D.Batista, A. G.2010-01-14T12:07:16Z2008-082008-08-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/2416eng0375-9601info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-22T17:06:50Zoai:run.unl.pt:10362/2416Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T16:37:58.495951Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv On the relation between the fractional Brownian motion and the fractional derivatives
title On the relation between the fractional Brownian motion and the fractional derivatives
spellingShingle On the relation between the fractional Brownian motion and the fractional derivatives
Ortigueira, M.D.
Forward and backward fractional derivatives
Generalised Cauchy derivative
Liouville derivative
Differintegration
Central fractional derivatives
Fractional stochastic process
Fractional Brownian motion
title_short On the relation between the fractional Brownian motion and the fractional derivatives
title_full On the relation between the fractional Brownian motion and the fractional derivatives
title_fullStr On the relation between the fractional Brownian motion and the fractional derivatives
title_full_unstemmed On the relation between the fractional Brownian motion and the fractional derivatives
title_sort On the relation between the fractional Brownian motion and the fractional derivatives
author Ortigueira, M.D.
author_facet Ortigueira, M.D.
Batista, A. G.
author_role author
author2 Batista, A. G.
author2_role author
dc.contributor.none.fl_str_mv RUN
dc.contributor.author.fl_str_mv Ortigueira, M.D.
Batista, A. G.
dc.subject.por.fl_str_mv Forward and backward fractional derivatives
Generalised Cauchy derivative
Liouville derivative
Differintegration
Central fractional derivatives
Fractional stochastic process
Fractional Brownian motion
topic Forward and backward fractional derivatives
Generalised Cauchy derivative
Liouville derivative
Differintegration
Central fractional derivatives
Fractional stochastic process
Fractional Brownian motion
description Physics Letters A, vol. 372; Issue 7
publishDate 2008
dc.date.none.fl_str_mv 2008-08
2008-08-01T00:00:00Z
2010-01-14T12:07:16Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/2416
url http://hdl.handle.net/10362/2416
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0375-9601
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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