任意维连续PAM及相关模型的势随机平移正则化
Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension
摘要：
研究了势沿分数布朗运动路径移动的连续抛物Anderson模型的噪声正则化现象。我们证明，只要Hurst参数选择足够小，这种转变允许建立适定性和稳定的相应的问题-而不需要重整化-在任何维度。此外，我们还提供了一个鲁棒Feynman-Kac型公式的正则化问题的唯一解决方案的建设上的局部时间的分数布朗运动以及非线性杨氏积分的正则性估计。
英文摘要：
We study a regularization by noise phenomenon for the continuous parabolic Anderson model with a potential shifted along paths of fractional Brownian motion. We demonstrate that provided the Hurst parameter is chosen sufficiently small, this shift allows to establish well-posedness and stability to the corresponding problem - without the need of renormalization - in any dimension. We moreover provide a robustified Feynman-Kac type formula for the unique solution to the regularized problem building upon regularity estimates for the local time of fractional Brownian motion as well as non-linear Young integration.
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