论文标题
在随机热方程式的besov规律性和本地时间
On Besov regularity and local time of the stochastic heat equation
论文作者
论文摘要
对时间和空间变量的规律进行了尖锐的规律，以$ \左（u（t，x），\; t \ in [0，t]，\; x \ in \ mathbb {r} \ right）$，这是对随机热方程式的轻度解决方案，由时空空间白噪声驱动。为$ u（t，x）$建立了当地时代的存在，Hölder的连续性和BESOV规律性，将其视为空间变量或时间变量中的过程。还获得了其相应水平集的Hausdorff尺寸。
Sharp Besov regularities in time and space variables are investigated for $\left(u(t,x),\; t\in [0,T],\; x\in \mathbb{R}\right)$, the mild solution to the stochastic heat equation driven by space-time white noise. Existence, Hölder continuity, and Besov regularity of local times are established for $u(t,x)$ viewed either as a process in the space variable or time variable. Hausdorff dimensions of their corresponding level sets are also obtained.
