Fractional Gaussian Noise : Projections, Prediction, Norms

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dc.contributor.authorBodnarchuk, Iryna
dc.contributor.authorMishura, Yuliya
dc.contributor.authorRalchenko, Kostiantyn
dc.contributor.departmentfi=Ei tutkimusalustaa|en=No platform|
dc.contributor.facultyfi=Tekniikan ja innovaatiojohtamisen yksikkö|en=School of Technology and Innovations|
dc.contributor.orcidhttps://orcid.org/0000-0001-7208-3130
dc.date.accessioned2025-08-27T07:09:04Z
dc.date.issued2025-06-29
dc.description.abstractWe examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst index and the number of neighboring elements used for the projection. We derive recurrence relations for the coefficients of the two-sided projection. Additionally, we explore the norms of both types of projections. Certain special cases are investigated in greater detail, both theoretically and numerically.
dc.description.notification© 2025 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 (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
dc.description.reviewstatusfi=vertaisarvioitu|en=peerReviewed|
dc.format.contentfi=kokoteksti|en=fulltext|
dc.format.extent26
dc.identifier.urihttps://osuva.uwasa.fi/handle/11111/18952
dc.identifier.urnURN:NBN:fi-fe2025082784709
dc.language.isoeng
dc.publisherMDPI
dc.relation.doi10.3390/fractalfract9070428
dc.relation.funderThe Swedish Foundation for Strategic Research
dc.relation.funderJapan Science and Technology Agency CREST
dc.relation.funderResearch Council of Finland
dc.relation.funderResearch Council of Norway
dc.relation.grantnumberUKR24-0004
dc.relation.grantnumberJPMJCR2115
dc.relation.grantnumber367468
dc.relation.grantnumber274410
dc.relation.ispartofjournalFractal and Fractional
dc.relation.issn2504-3110
dc.relation.issue7
dc.relation.urlhttps://doi.org/10.3390/fractalfract9070428
dc.relation.volume9
dc.rightsCC BY 4.0
dc.source.identifierWOS:001535588500001
dc.source.identifier2-s2.0-105011840712
dc.subjectfractional Brownian motion
dc.subjectfractional Gaussian noise
dc.subjectcoefficients of projection
dc.subjectprediction coefficients
dc.subjectL2-norm
dc.subjectautocovariance function
dc.subject.disciplinefi=Matematiikka|en=Mathematics|
dc.titleFractional Gaussian Noise : Projections, Prediction, Norms
dc.type.okmfi=A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä|en=A1 Peer-reviewed original journal article|sv=A1 Originalartikel i en vetenskaplig tidskrift|
dc.type.publicationarticle
dc.type.versionpublishedVersion

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