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Article: Recent advances on eigenvalues of matrix-valued stochastic processes

TitleRecent advances on eigenvalues of matrix-valued stochastic processes
Authors
KeywordsBrownian sheets
Dyson Brownian motion
Eigenvalue distribution
Fractional Brownian motion
Matrix-valued process
Issue Date2022
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmva
Citation
Journal of Multivariate Analysis, 2022, v. 188, p. article no. 104847 How to Cite?
AbstractSince the introduction of Dyson’s Brownian motion in early 1960s, there have been a lot of developments in the investigation of stochastic processes on the space of Hermitian matrices. Their properties, especially, the properties of their eigenvalues have been studied in great detail. In particular, the limiting behaviours of the eigenvalues are found when the dimension of the matrix space tends to infinity, which connects with random matrix theory. This survey reviews a selection of results on the eigenvalues of stochastic processes from the literature of the past three decades. For most recent variations of such processes, such as matrix-valued processes driven by fractional Brownian motion or Brownian sheet, the eigenvalues of them are also discussed in this survey. In the end, some open problems in the area are also proposed.
Persistent Identifierhttp://hdl.handle.net/10722/310519
ISSN
2023 Impact Factor: 1.4
2023 SCImago Journal Rankings: 0.837
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorSong, J-
dc.contributor.authorYao, J-
dc.contributor.authorYUAN, W-
dc.date.accessioned2022-02-07T07:57:50Z-
dc.date.available2022-02-07T07:57:50Z-
dc.date.issued2022-
dc.identifier.citationJournal of Multivariate Analysis, 2022, v. 188, p. article no. 104847-
dc.identifier.issn0047-259X-
dc.identifier.urihttp://hdl.handle.net/10722/310519-
dc.description.abstractSince the introduction of Dyson’s Brownian motion in early 1960s, there have been a lot of developments in the investigation of stochastic processes on the space of Hermitian matrices. Their properties, especially, the properties of their eigenvalues have been studied in great detail. In particular, the limiting behaviours of the eigenvalues are found when the dimension of the matrix space tends to infinity, which connects with random matrix theory. This survey reviews a selection of results on the eigenvalues of stochastic processes from the literature of the past three decades. For most recent variations of such processes, such as matrix-valued processes driven by fractional Brownian motion or Brownian sheet, the eigenvalues of them are also discussed in this survey. In the end, some open problems in the area are also proposed.-
dc.languageeng-
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmva-
dc.relation.ispartofJournal of Multivariate Analysis-
dc.subjectBrownian sheets-
dc.subjectDyson Brownian motion-
dc.subjectEigenvalue distribution-
dc.subjectFractional Brownian motion-
dc.subjectMatrix-valued process-
dc.titleRecent advances on eigenvalues of matrix-valued stochastic processes-
dc.typeArticle-
dc.identifier.emailYao, J: jeffyao@hku.hk-
dc.identifier.authorityYao, J=rp01473-
dc.description.naturelink_to_OA_fulltext-
dc.identifier.doi10.1016/j.jmva.2021.104847-
dc.identifier.scopuseid_2-s2.0-85118259929-
dc.identifier.hkuros331634-
dc.identifier.volume188-
dc.identifier.spagearticle no. 104847-
dc.identifier.epagearticle no. 104847-
dc.identifier.isiWOS:000759646700028-
dc.publisher.placeUnited States-

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