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Asymptotic behavior of the solution of the fractional heat equation

Author

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  • Yan, Litan
  • Yu, Xianye
  • Sun, Xichao

Abstract

In this short note, we study the asymptotic behavior of the solution to the fractional heat equation ∂u∂t(t,x)=−(−Δ)α/2u(t,x)+u(t,x)∂d+1W∂t∂x1⋯∂xd,t>0,x∈Rd with initial condition bounded above and below, where α∈(0,2) and the noise W(t,x) is a fractional Brownian sheet. The method of moments is used to investigate the solution.

Suggested Citation

  • Yan, Litan & Yu, Xianye & Sun, Xichao, 2016. "Asymptotic behavior of the solution of the fractional heat equation," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 54-61.
    • Handle: RePEc:eee:stapro:v:117:y:2016:i:c:p:54-61
    DOI: 10.1016/j.spl.2016.05.004
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    References listed on IDEAS

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    1. Song, Jian, 2012. "Asymptotic behavior of the solution of heat equation driven by fractional white noise," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 614-620.
    2. Balan, Raluca M. & Conus, Daniel, 2014. "A note on intermittency for the fractional heat equation," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 6-14.
    3. Chen, Xia & Rosen, Jay, 2010. "Large deviations and renormalization for Riesz potentials of stable intersection measures," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1837-1878, August.
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    Cited by:

    1. Litan Yan & Xianye Yu, 2019. "Asymptotic Behavior for High Moments of the Fractional Heat Equation with Fractional Noise," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1617-1646, December.

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