论文标题
Sierpinski垫片和相关分形上的分数高斯田地
Fractional Gaussian fields on the Sierpinski gasket and related fractals
论文作者
论文摘要
我们在SierpińskiGasket $ k $上定义和研究了配备其Hausdorff量的SierpińskiGasket $ k $的Hurst参数$ h $的分数高斯字段$ x $。从薄弱的意义上讲，它是方程式$（ - δ）^s x = w $的解决方案，其中$ w $是$ l_0^2（k，μ）$，$δ$ $ k $和$ k $和$ s = \ s = \ frac {d_h+2h+2h} $，$ k $ k $ l _0^2（k，μ）上的高斯白噪声， $ d_w $它的步行维度。然后将这些田地的建设扩展到其他分形，包括Sierpiński地毯。
We define and study a fractional Gaussian field $X$ with Hurst parameter $H$ on the Sierpiński gasket $K$ equipped with its Hausdorff measure $μ$. It appears as a solution, in a weak sense, of the equation $(-Δ)^s X =W$ where $W$ is a Gaussian white noise on $L_0^2(K,μ)$, $Δ$ the Laplacian on $K$ and $s= \frac{d_h+2H}{2d_w}$, where $d_h$ is the Hausdorff dimension of $K$ and $d_w$ its walk dimension. The construction of those fields is then extended to other fractals including the Sierpiński carpet.
