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    Stochastic calculus for fractional Brownian motion - I. Theory

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    Issue Date
    2000-02-02
    Author
    Duncan, Tyrone E.
    Hu, Yaozhong
    Pasik-Duncan, Bozenna
    Publisher
    SIAM PUBLICATIONS
    Format
    323285 bytes
    Type
    Article
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    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.
    URI
    http://hdl.handle.net/1808/278
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    • Mathematics Scholarly Works [282]
    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.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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