通过Hölder曲线的首次通过时间密度
First Passage Time Densities through Hölder curves
摘要：
证明了对于标准布朗运动，存在通过指数大于1/2的局部Hölder连续曲线的首次通过时间密度函数.利用标准布朗运动局部时的一个性质和Cannon [2]中的偏微分方程理论，得到了密度函数存在的一个充分条件.我们还证明了这个密度函数与具有Dirichlet边界条件的热方程在移动边界处的格林函数的空间导数成正比。
英文摘要：
We prove that for a standard Brownian motion, there exists a first-passage-time density function through a locally Hölder continuous curve with exponent greater than 1/2. By using a property of local time of a standard Brownian motion and the theories of partial differential equations in Cannon [2], we find a sufficient condition for existence of the density function. We also show that this density function is proportional to the space derivative of the Green function of the heat equation with Dirichlet boundary condition at the moving boundary.
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