论文标题
通过随机翻译在任意维度中的连续PAM和相关模型的电势进行正则化
Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension
论文作者
论文摘要
我们研究连续抛物线模型的噪声现象的正则化，并沿分数布朗运动的路径移动。我们证明，只要选择了足够小的赫斯特参数，这种转变允许在任何维度中建立适当的和稳定的对相应问题的稳定性 - 而无需重新规定。此外，我们提供了一个可靠的Feynman-KAC类型公式，以根据分数布朗运动的本地时间以及非线性的Young整合的定期估计，以实现正规化问题的唯一解决方案。
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.
