On Short Time Asymptotic Behavior of Some Symmetric Diffusions on General State Spaces
On Short Time Asymptotic Behavior of Some Symmetric Diffusions on General State Spaces
复制标题
一般状态空间上某些对称扩散的短时渐近行为
DOI：
10.1023/a:1014033208581
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发表时间：
2002
影响因子：
1.1
通讯作者：
M. Hino
中科院分区：
文献类型：
--
作者：
M. Hino
对于一般状态空间（X，m）上的保守对称扩散，研究了tlog <$X1A <$Tt1Bdm的短时渐近行为，其中Tt是相伴半群，A和B是X的可测子集.证明了在一定的绝对常数下，下极限支配上级极限。当相应Dirichlet型的Γ2有下界时，证明了对任意A和B都存在极限，并由它们之间的内禀度量描述.应用到无限维空间和分形。
For conservative symmetric diffusions on a general state space (X,m), the short time asymptotic behavior of tlog∫X1A⋅Tt1B dm is investigated, where Tt is the associated semigroup and A and B are measurable subsets of X. It is proved that the superior limit is dominated by the inferior limit up to some absolute constant. When Γ2 of the associated Dirichlet form is lower bounded, it is shown that the limit exists for any A and B, and is described by the intrinsic metric between them. Applications to infinite-dimensional spaces and fractals are given.