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Hölder continuity for stochastic fractional heat equation with colored noise

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  • Li, Kexue

Abstract

In this paper, we consider semilinear stochastic fractional heat equation ∂ut∂t=−(−△)β/2ut+σ(ut)η̇. The Gaussian noise η̇ is assumed to be colored in space with covariance of the form E(η̇(t,x)η̇(s,y))=δ0(t−s)fα(x−y), where fα is the Riesz kernel fα(x)∝∣x∣−α. We obtain the spatial and temporal Hölder continuity of the mild solution.

Suggested Citation

  • Li, Kexue, 2017. "Hölder continuity for stochastic fractional heat equation with colored noise," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 34-41.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:34-41
    DOI: 10.1016/j.spl.2017.04.020
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    References listed on IDEAS

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    1. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
    2. Song, Jian, 2017. "On a class of stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 37-79.
    3. Hu, Yaozhong & Nualart, David & Song, Jian, 2013. "A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1083-1103.
    4. Bezdek, Pavel, 2016. "On weak convergence of stochastic heat equation with colored noise," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2860-2875.
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