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Homogenization for singularly perturbed stochastic wave equations with Hölder continuous coefficients

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  • Yang, Li

Abstract

This work is concerned with the homogenization problem for singularly perturbed stochastic wave equations. Under the assumption that the coefficients are only Hölder continuous, we prove the weak convergence of the original system to a limit equation with an extra Gaussian term by using the technique of Poisson equation in Hilbert space. The optimal convergence rate is also obtained.

Suggested Citation

  • Yang, Li, 2025. "Homogenization for singularly perturbed stochastic wave equations with Hölder continuous coefficients," Statistics & Probability Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002281
    DOI: 10.1016/j.spl.2024.110259
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    References listed on IDEAS

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    1. Fu, Hongbo & Wan, Li & Liu, Jicheng & Liu, Xianming, 2018. "Weak order in averaging principle for stochastic wave equation with a fast oscillation," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2557-2580.
    2. Wang, Ruifang & Xu, Yong & Yue, Hongge, 2022. "Stochastic averaging for the non-autonomous mixed stochastic differential equations with locally Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 182(C).
    3. Barbu, Viorel & Da Prato, Giuseppe & Tubaro, Luciano, 2007. "Stochastic wave equations with dissipative damping," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1001-1013, August.
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