dc.contributor.author Duncan, Tyrone E. dc.contributor.author Hu, Yaozhong dc.contributor.author Pasik-Duncan, Bozenna dc.date.accessioned 2005-04-11T18:25:26Z dc.date.available 2005-04-11T18:25:26Z dc.date.issued 2000-02-02 dc.identifier.citation Duncan, 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.other ISI:000085672100011 dc.identifier.other http://www.siam.org/journals/sicon/sicon.htm dc.identifier.uri http://hdl.handle.net/1808/278 dc.description.abstract In 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.sponsorship Research partially funded by NSF Grant DMS 9623439 dc.format.extent 323285 bytes dc.format.mimetype application/pdf dc.language.iso en_US dc.publisher SIAM PUBLICATIONS dc.subject Fractional brownian motion dc.subject Multiple stratonovich integrals dc.subject Multiple ito integrals dc.subject Ito calculus dc.subject Stochastic calculus dc.subject Ito integral dc.subject Stratonovich integra dc.subject Ito formula dc.subject Wick product dc.title Stochastic calculus for fractional Brownian motion - I. Theory dc.type Article dc.rights.accessrights openAccess
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