Construction of diffusion processes on fractals, $d$-sets, and general metric measure spaces
Construction of diffusion processes on fractals, $d$-sets, and general metric measure spaces
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DOI：
10.1215/kjm/1250281992
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发表时间：
2005
影响因子：
--
通讯作者：
T. Kumagai;Karl-Theodor Sturm
中科院分区：
文献类型：
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作者：
T. Kumagai;Karl-Theodor Sturm
给出了局部紧可分度量测度空间（M，ρ，μ）上构造非平凡μ-对称扩散过程的一个充分条件.这些过程与局部正则Dirichlet形式相关联，局部正则Dirichlet形式作为逼近非局部Dirichlet形式的Γ-极限的连续部分而获得。对于各种分形，我们可以使用现有的估计来验证我们的假设。这表明我们构造扩散的一般方法可以应用于这些分形。
We give a sufficient condition to construct non-trivial µ-symmetric diffusion processes on a locally compact separable metric measure space (M, ρ, µ). These processes are associated with local regular Dirichlet forms which are obtained as continuous parts of Γ-limits for approximating non-local Dirichlet forms. For various fractals, we can use existing estimates to verify our assumptions. This shows that our general method of constructing diffusions can be applied to these fractals.