论文标题
抛物线安德森模型在太空和粗糙的初始条件中具有粗糙的噪音
Parabolic Anderson model with rough noise in space and rough initial conditions
论文作者
论文摘要
In this note, we consider the parabolic Anderson model on $\mathbb{R}_{+} \times \mathbb{R}$, driven by a Gaussian noise which is fractional in time with index $H_0>1/2$ and fractional in space with index $0<H<1/2$ such that $H_0+H>3/4$.在初始数据的一般条件下，我们证明了温和解决方案的存在和独特性，并在所有$ p $ p $ p \ ge 2 $的所有$ p $ thements上获得了指数上限。
In this note, we consider the parabolic Anderson model on $\mathbb{R}_{+} \times \mathbb{R}$, driven by a Gaussian noise which is fractional in time with index $H_0>1/2$ and fractional in space with index $0<H<1/2$ such that $H_0+H>3/4$. Under a general condition on the initial data, we prove the existence and uniqueness of the mild solution and obtain its exponential upper bounds in time for all $p$-th moments with $p\ge 2$.
