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<p>This short note is devoted to establishing the almost sure central limit theorem for the parabolic/hyperbolic Anderson models driven by colored-in-time Gaussian noises, completing recent results on quantitative central limit theorems for stochastic partial differential equations. We combine the second-order Gaussian Poincaré inequality with the method of characteristic functions of Ibragimov and Lifshits, effectively overcoming the challenge from the lack of Itô tools in this colored-in-time setting, and achieving results that are inaccessible with previous methods.</p>

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Almost Sure Central Limit Theorems for Parabolic/Hyperbolic Anderson Models with Gaussian Colored Noises

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月28日

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  • Panqiu Xia,
  • Guangqu Zheng

摘要

This short note is devoted to establishing the almost sure central limit theorem for the parabolic/hyperbolic Anderson models driven by colored-in-time Gaussian noises, completing recent results on quantitative central limit theorems for stochastic partial differential equations. We combine the second-order Gaussian Poincaré inequality with the method of characteristic functions of Ibragimov and Lifshits, effectively overcoming the challenge from the lack of Itô tools in this colored-in-time setting, and achieving results that are inaccessible with previous methods.