We construct a K-rough path [along the terminology of Deya (Probab Theory Relat Fields 166:1–65, 2016)] above either a space-time or a spatial fractional Brownian motion, in any space dimension d. This allows us to provide an interpretation and a unique solution for the corresponding parabolic Anderson model, understood in the renormalized sense. We also consider the case of a spatial fractional noise.

中文翻译：

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AK-时空分数布朗运动以上的粗糙路径

我们在任意时空d或时空或空间分数布朗运动上方构造一个K粗糙路径[沿Deya的术语（Probab理论相关领域166：1-65，2016）] 。这使我们能够为相应的抛物线安德森模型提供解释和独特的解决方案，以重新归一化的意义进行理解。我们还考虑了空间分数噪声的情况。