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Article: Fractional martingales and characterization of the fractional Brownian motion
Title | Fractional martingales and characterization of the fractional Brownian motion |
---|---|
Authors | |
Keywords | Β-Variation Fractional Brownian Motion Fractional Martingale Lévy's Characterization Theorem |
Issue Date | 2009 |
Citation | Annals Of Probability, 2009, v. 37 n. 6, p. 2404-2430 How to Cite? |
Abstract | In 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 Identifier | http://hdl.handle.net/10722/180467 |
ISSN | 2023 Impact Factor: 2.1 2023 SCImago Journal Rankings: 3.203 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Hu, Y | en_US |
dc.contributor.author | Nualart, D | en_US |
dc.contributor.author | Song, J | en_US |
dc.date.accessioned | 2013-01-28T01:38:29Z | - |
dc.date.available | 2013-01-28T01:38:29Z | - |
dc.date.issued | 2009 | en_US |
dc.identifier.citation | Annals Of Probability, 2009, v. 37 n. 6, p. 2404-2430 | en_US |
dc.identifier.issn | 0091-1798 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/180467 | - |
dc.description.abstract | In 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.language | eng | en_US |
dc.relation.ispartof | Annals of Probability | en_US |
dc.subject | Β-Variation | en_US |
dc.subject | Fractional Brownian Motion | en_US |
dc.subject | Fractional Martingale | en_US |
dc.subject | Lévy's Characterization Theorem | en_US |
dc.title | Fractional martingales and characterization of the fractional Brownian motion | en_US |
dc.type | Article | en_US |
dc.identifier.email | Song, J: txjsong@hku.hk | en_US |
dc.identifier.authority | Song, J=rp01700 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1214/09-AOP464 | en_US |
dc.identifier.scopus | eid_2-s2.0-77049095363 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-77049095363&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 37 | en_US |
dc.identifier.issue | 6 | en_US |
dc.identifier.spage | 2404 | en_US |
dc.identifier.epage | 2430 | en_US |
dc.identifier.isi | WOS:000272499500011 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Hu, Y=7407117772 | en_US |
dc.identifier.scopusauthorid | Nualart, D=7004476842 | en_US |
dc.identifier.scopusauthorid | Song, J=55489918300 | en_US |
dc.identifier.issnl | 0091-1798 | - |