具有高斯彩色噪声的抛物线/超抛物线安德森模型的几乎确定的中心极限定理

Panqiu Xia, Guangqu Zheng
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引用次数: 0

摘要

这篇短文致力于建立由有色高斯噪声驱动的抛物/超抛物安德森模型的几乎确定的中心极限定理,完成了最近关于随机偏微分方程定量中心极限定理的成果。我们将这些二阶高斯 Poincar\'e 不等式与 Ibragimov 和 Lifshits 的特征函数方法结合起来,有效地克服了在这种有色-时间设置中缺乏 It\^o 工具所带来的挑战,并获得了以前的方法无法获得的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Almost sure central limit theorems for parabolic/hyperbolic Anderson models with Gaussian colored noises
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 Poincar\'e inequality with Ibragimov and Lifshits' method of characteristic functions, effectively overcoming the challenge from the lack of It\^o tools in this colored-in-time setting, and achieving results that are inaccessible with previous methods.
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