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    Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter H < 1/2

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    NualartD_AP_40(3)1041.pdf (250.1Kb)
    Issue Date
    2012-09-01
    Author
    Hu, Yaozhong
    Lu, Fei
    Nulart, David
    Publisher
    Institute of Mathematical Statistics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
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    Abstract
    In this paper, a Feynman–Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter H < 1/2. To establish such a formula, we introduce and study a nonlinear stochastic integral from the given Gaussian noise. To show the Feynman–Kac integral exists, one still needs to show the exponential integrability of nonlinear stochastic integral. Then, the approach of approximation with techniques from Malliavin calculus is used to show that the Feynman–Kac integral is the weak solution to the stochastic partial differential equation.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1214/11-AOP649.
    URI
    http://hdl.handle.net/1808/17012
    DOI
    https://doi.org/10.1214/11-AOP649
    Collections
    • Mathematics Scholarly Works [283]
    Citation
    Hu, Yaozhong., Lu, Fei., Nualart, David. "Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter H < 1/2." Ann. Probab. Volume 40, Number 3 (2012), 1041-1068. http://dx.doi.org/10.1214/11-AOP649.

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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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