Long Time Behavior of the Volume of the Wiener Sausage on Dirichlet Spaces
Long Time Behavior of the Volume of the Wiener Sausage on Dirichlet Spaces
复制标题
DOI：
10.1007/s11118-018-9738-y
复制
发表时间：
2018-03
影响因子：
1.1
通讯作者：
K. Okamura
中科院分区：
文献类型：
--
作者：
K. Okamura
本文考虑Dirichlet空间上Wiener香肠体积的长时间行为。我们专注于体积的Wiener香肠的度量测度空间以外的欧几里得空间配备的勒贝格测度的扩散过程。在满足Ahlfors正则性和次高斯热核估计的度量测度Dirichlet空间上，得到了Wiener香肠体积的期望增长率和几乎必然行为.我们表明，增长率的期望上的有界修改的欧几里得空间是相同的欧几里得空间配备了勒贝格测度。我们给出一个度量测度狄利克雷空间的一个例子，其上的尺度的手段波动。
In the present paper, we consider long time behaviors of the volume of the Wiener sausage on Dirichlet spaces. We focus on the volume of the Wiener sausage for diffusion processes on metric measure spaces other than the Euclid space equipped with the Lebesgue measure. We obtain the growth rate of the expectations and almost sure behaviors of the volumes of the Wiener sausages on metric measure Dirichlet spaces satisfying Ahlfors regularity and sub-Gaussian heat kernel estimates. We show that the growth rate of the expectations on a bounded modification of the Euclidian space is identical with the one on the Euclidian space equipped with the Lebesgue measure. We give an example of a metric measure Dirichlet space on which a scaled of the means fluctuates.