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Weak Convergence for the Fourth-Order Stochastic Heat Equation with Fractional Noises

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Abstract

In this paper, we study a fourth-order stochastic heat equation with homogeneous Neumann boundary conditions and double-parameter fractional noises. We formally replace the random perturbation by a family of noisy inputs depending on a parameter \(n\in {\mathbb {N}}\) which approximates the noises. Then we provided sufficient conditions ensuring that the real-valued mild solution of the fourth-order stochastic heat equation driven by this family of noises converges in law, in the space of \(C([0,T]\times [0,\pi ])\) of continuous functions, to the solution of a class of fourth-order stochastic heat equation driven by fractional noises.

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Acknowledgements

We want to thank the Editor and anonymous referees whose valuable remarks and suggestions greatly improved the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China

    Junfeng Liu

  2. Department of Statistics, Nanjing Audit University, Nanjing, 211815, People’s Republic of China

    Junfeng Liu & Yang Yang

  3. Department of Mathematics, Anhui Normal University, Wuhu, 241000, People’s Republic of China

    Guangjun Shen

Authors
  1. Junfeng Liu
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  2. Guangjun Shen
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  3. Yang Yang
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Corresponding author

Correspondence to Junfeng Liu.

Additional information

Communicated by Lee See Keong.

Junfeng Liu is partially supported by NSFC (11401313), NSFJS (BK20161579), NSF of Jiangsu Educational Committee (14KJB110013), CPSF (Nos. 2014M560368, 2015T80475), Qing Lan Project, Jiangsu Planned Projects for Postdoctoral Research Funds (1401011C). Guangjun Shen is partially supported by NSFC (11271020) the Distinguished Young Scholars Foundation of Anhui Province (1608085J06). Yang Yang is partially supported by NSFC (71471090).

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Liu, J., Shen, G. & Yang, Y. Weak Convergence for the Fourth-Order Stochastic Heat Equation with Fractional Noises. Bull. Malays. Math. Sci. Soc. 40, 565–582 (2017). https://doi.org/10.1007/s40840-017-0457-0

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  • DOI: https://doi.org/10.1007/s40840-017-0457-0

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