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    Feynman-Kac formula for the heat equation driven by fractional white noise

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    NualartD_AP_39(1)291.pdf (302.2Kb)
    Issue Date
    2011-02-01
    Author
    Hu, Yaozhong
    Nualart, David
    Song, Jian
    Publisher
    Institute of Mathematical Statistics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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    Abstract
    We establish a version of the Feynman–Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the Feynman–Kac formula is a weak solution of the stochastic heat equation. From the Feynman–Kac formula, we establish the smoothness of the density of the solution and the Hölder regularity in the space and time variables. We also derive a Feynman–Kac formula for the stochastic heat equation in the Skorokhod sense and we obtain the Wiener chaos expansion of the solution.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1214/10-AOP547.
    URI
    http://hdl.handle.net/1808/17017
    DOI
    https://doi.org/10.1214/10-AOP547
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Hu, Yaozhong., Nualart, David., Song, Jian. "Feynman–Kac formula for heat equation driven by fractional white noise." Ann. Probab. Volume 39, Number 1 (2011), 291-326. http://dx.doi.org/10.1214/10-AOP547.

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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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