In this paper, we concern the fourth parabolic model on ℝ driven by a multiplicative Gaussian noise which behaves like fractional Brownian motion in time and space with Hurst index 1 2 < H0 < 1 and 0 < H1 < 1 2, respectively. The existence and uniqueness of mild solution in Skorohod sense are proved, and the weak intermittency is obtained by estimating pth (p ≥ 2) moment of the solution. Moreover, the Hölder continuity can be obtained for the time and space variable.

中文翻译：

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空间粗噪声驱动的高阶安德森抛物线模型

在本文中，我们关注第四个抛物线模型ℝ由乘性高斯噪声驱动，其行为类似于具有赫斯特指数的时间和空间上的分数布朗运动1 2 < H0 < 1和0 < H1 < 1 2， 分别。证明了Skorohod意义上温和解的存在性和唯一性，通过估计得到弱间歇性pth (p ≥ 2) 解的时刻。此外，对于时间和空间变量，可以得到 Hölder 连续性。