稳定过程基态本征函数的形状
On the shape of the ground state eigenfunction for stable processes
摘要：
我们证明了在离开$(-1, 1)$区间时被杀死的$α\in (0, 2)$阶对称稳定过程的基态本征函数在$(-{1/2}, {1/2})$上是凹的。我们称之为“中...中...”。类似的语句适用于$\R^d$、$d>1$中的矩形。这些结果来自于有限维布朗运动和从属分布的类似结果。
英文摘要：
We prove that the ground state eigenfunction for symmetric stable processes of order $α\in (0, 2)$ killed upon leaving the interval $(-1, 1)$ is concave on $(-{1/2}, {1/2})$. We call this property "mid--concavity." A similar statement holds for rectangles in $\R^d$, $d>1$. These result follow from similar results for finite dimensional distributions of Brownian motion and subordination.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
