ATTENTION: The software behind KU ScholarWorks is being upgraded to a new version. Starting July 15th, users will not be able to log in to the system, add items, nor make any changes until the new version is in place at the end of July. Searching for articles and opening files will continue to work while the system is being updated. If you have any questions, please contact Marianne Reed at mreed@ku.edu .

Show simple item record

Stochastic calculus for fractional Brownian motion - I. Theory

dc.contributor.authorDuncan, Tyrone E.
dc.contributor.authorHu, Yaozhong
dc.contributor.authorPasik-Duncan, Bozenna
dc.date.accessioned2005-04-11T18:25:26Z
dc.date.available2005-04-11T18:25:26Z
dc.date.issued2000-02-02
dc.identifier.citationDuncan, TE; Hu, YZ; Pasik-Duncan, B. Stochastic calculus for fractional Brownian motion - I. Theory. SIAM JOURNAL ON CONTROL AND OPTIMIZATION. Feb 2 2000.38(2):582-612.
dc.identifier.otherISI:000085672100011
dc.identifier.otherhttp://www.siam.org/journals/sicon/sicon.htm
dc.identifier.urihttp://hdl.handle.net/1808/278
dc.description.abstractIn this paper a stochastic calculus is given for the fractional Brownian motions that have the Hurst parameter in (1/2, 1). A stochastic integral of Ito type is defined for a family of integrands so that the integral has zero mean and an explicit expression for the second moment. This integral uses the Wick product and a derivative in the path space. Some Ito formulae (or change of variables formulae) are given for smooth functions of a fractional Brownian motion or some processes related to a fractional Brownian motion. A stochastic integral of Stratonovich type is defined and the two types of stochastic integrals are explicitly related. A square integrable functional of a fractional Brownian motion is expressed as an infinite series of orthogonal multiple integrals.
dc.description.sponsorshipResearch partially funded by NSF Grant DMS 9623439
dc.format.extent323285 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherSIAM PUBLICATIONS
dc.subjectFractional brownian motion
dc.subjectMultiple stratonovich integrals
dc.subjectMultiple ito integrals
dc.subjectIto calculus
dc.subjectStochastic calculus
dc.subjectIto integral
dc.subjectStratonovich integra
dc.subjectIto formula
dc.subjectWick product
dc.titleStochastic calculus for fractional Brownian motion - I. Theory
dc.typeArticle
dc.rights.accessrightsopenAccess


Files in this item

Thumbnail
Name:
dhp.pdf
Size:
315.7Kb
Format:
PDF
View/Open

This item appears in the following Collection(s)

Show simple item record