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Article: Fractional martingales and characterization of the fractional Brownian motion

TitleFractional martingales and characterization of the fractional Brownian motion
Authors
Hu, YNualart, DSong, J
KeywordsΒ-Variation
Fractional Brownian Motion
Fractional Martingale
Lévy's Characterization Theorem
Issue Date2009
Citation
Annals Of Probability, 2009, v. 37 n. 6, p. 2404-2430 How to Cite?
DOI: http://dx.doi.org/10.1214/09-AOP464
AbstractIn this paper we introduce the notion of fractional martingale as the fractional derivative of order α of a continuous local martingale, where α ε (-1/2,1/2), and we show that it has a nonzero finite variation of order,2/1+2α under some integrability assumptions on the quadratic variation of the local martingale. As an application we establish an extension of Lévy's characterization theorem for the fractional Brownian motion. © Institute of Mathematical Statistics, 2009.
Persistent Identifierhttp://hdl.handle.net/10722/180467
ISSN
0091-1798
2021 Impact Factor: 2.288
2020 SCImago Journal Rankings: 3.184
ISI Accession Number ID
WOS:000272499500011
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorHu, Yen_US
dc.contributor.authorNualart, Den_US
dc.contributor.authorSong, Jen_US
dc.date.accessioned2013-01-28T01:38:29Z-
dc.date.available2013-01-28T01:38:29Z-
dc.date.issued2009en_US
dc.identifier.citationAnnals Of Probability, 2009, v. 37 n. 6, p. 2404-2430en_US
dc.identifier.issn0091-1798en_US
dc.identifier.urihttp://hdl.handle.net/10722/180467-
dc.description.abstractIn this paper we introduce the notion of fractional martingale as the fractional derivative of order α of a continuous local martingale, where α ε (-1/2,1/2), and we show that it has a nonzero finite variation of order,2/1+2α under some integrability assumptions on the quadratic variation of the local martingale. As an application we establish an extension of Lévy's characterization theorem for the fractional Brownian motion. © Institute of Mathematical Statistics, 2009.en_US
dc.languageengen_US
dc.relation.ispartofAnnals of Probabilityen_US
dc.subjectΒ-Variationen_US
dc.subjectFractional Brownian Motionen_US
dc.subjectFractional Martingaleen_US
dc.subjectLévy's Characterization Theoremen_US
dc.titleFractional martingales and characterization of the fractional Brownian motionen_US
dc.typeArticleen_US
dc.identifier.emailSong, J: txjsong@hku.hken_US
dc.identifier.authoritySong, J=rp01700en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1214/09-AOP464en_US
dc.identifier.scopuseid_2-s2.0-77049095363en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77049095363&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume37en_US
dc.identifier.issue6en_US
dc.identifier.spage2404en_US
dc.identifier.epage2430en_US
dc.identifier.isiWOS:000272499500011-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridHu, Y=7407117772en_US
dc.identifier.scopusauthoridNualart, D=7004476842en_US
dc.identifier.scopusauthoridSong, J=55489918300en_US
dc.identifier.issnl0091-1798-

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