Weak convergence of symmetric diffusion processes
Weak convergence of symmetric diffusion processes
复制标题
对称扩散过程的弱收敛性
DOI：
10.1007/s004400050129
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发表时间：
1997
影响因子：
2
通讯作者：
T. Uemura
中科院分区：
文献类型：
--
作者：
K. Kuwae;T. Uemura
在正则Dirichlet空间下，我们证明了具有局部一致椭圆性的Dirichlet形式的相对紧开集上Mosco意义上与部分形式相关的形式的收敛性和基态的局部一致有界性。在无限维的狄利克雷空间中，我们也得到了同样的结论。由此，我们得到了在初始分布的某些条件下的弱收敛性和K. Th中使用的（修正的）伪度量定义的球的体积的增长顺序。Sturm。
In this paper, we show the convergence of forms in the sense of Mosco associated with the part form on relatively compact open set of Dirichlet forms with locally uniform ellipticity and the locally uniform boundedness of ground states under regular Dirichlet space setting. We also get the same assertion under Dirichlet space in infinite dimensional setting. As a result of this, we get the weak convergence under some conditions on initial distributions and the growth order of the volume of the balls defined by (modified) pseudo metric used in K. Th. Sturm.