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A central limit theorem for the stochastic heat equation

Author

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  • Huang, Jingyu
  • Nualart, David
  • Viitasaari, Lauri

Abstract

We consider the one-dimensional stochastic heat equation driven by a multiplicative space–time white noise. We show that the spatial integral of the solution from −R to R converges in total variance distance to a standard normal distribution as R tends to infinity, after renormalization. We also show a functional version of this central limit theorem.

Suggested Citation

  • Huang, Jingyu & Nualart, David & Viitasaari, Lauri, 2020. "A central limit theorem for the stochastic heat equation," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7170-7184.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:12:p:7170-7184
    DOI: 10.1016/j.spa.2020.07.010
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    Cited by:

    1. Kuzgun, Sefika & Nualart, David, 2022. "Convergence of densities of spatial averages of stochastic heat equation," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 68-100.
    2. Li, Jingyu & Zhang, Yong, 2021. "An almost sure central limit theorem for the stochastic heat equation," Statistics & Probability Letters, Elsevier, vol. 177(C).
    3. Balan, Raluca M. & Yuan, Wangjun, 2022. "Spatial integral of the solution to hyperbolic Anderson model with time-independent noise," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 177-207.

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