粗糙噪声驱动下抛物型Anderson模型的空间平均

arXiv: Probability Pub Date : 2020-10-12 DOI:10.30757/ALEA.V18-33

D. Nualart, Xiaoming Song, Guangqu Zheng

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引用次数: 11

摘要

本文研究了粗糙高斯噪声驱动下的抛物型Anderson模型在Skorohod意义上的空间平均。我们考虑了时间参数为$H_0$、空间参数为$H_1$的分数阶噪声，满足$H_0 \in(1/2,1)$、$H_1\in(0,1/2)$和$H_0 + H_1 > 3/4$。我们的主要结果是空间平均值的一个泛函中心极限定理。作为我们分析的一个重要组成部分，我们提出了一个新的关于赫斯特参数值的费曼-卡茨公式。

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Spatial averages for the parabolic Anderson model driven by rough noise

In this paper, we study spatial averages for the parabolic Anderson model in the Skorohod sense driven by rough Gaussian noise, which is colored in space and time. We include the case of a fractional noise with Hurst parameters $H_0$ in time and $H_1$ in space, satisfying $H_0 \in (1/2,1)$, $H_1\in (0,1/2)$ and $H_0 + H_1 > 3/4$. Our main result is a functional central limit theorem for the spatial averages. As an important ingredient of our analysis, we present a Feynman-Kac formula that is new for these values of the Hurst parameters.

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arXiv: Probability

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