论文标题
Hausdorff的量度和水平集的高斯随机场的范围和水平集，具有部门局部非确定性
The Hausdorff measure of the range and level sets of Gaussian random fields with sectorial local nondeterminism
论文作者
论文摘要
我们确定了满足部门局部非确定性和其他假设的高斯随机场的范围和水平集的确切hausdorff测量函数。我们还建立了迭代对数的chung型法律。结果可以应用于布朗片，分数布朗尼片，其赫斯特指数在所有方向上都是相同的，以及一个由时空白噪声或彩色噪声驱动的一个空间尺寸的线性随机波方程的系统。
We determine the exact Hausdorff measure functions for the range and level sets of a class of Gaussian random fields satisfying sectorial local nondeterminism and other assumptions. We also establish a Chung-type law of the iterated logarithm. The results can be applied to the Brownian sheet, fractional Brownian sheets whose Hurst indices are the same in all directions, and systems of linear stochastic wave equations in one spatial dimension driven by space-time white noise or colored noise.
