On Short Time Asymptotic Behavior of Some Symmetric Diffusions on General State Spaces |
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Authors: | Masanori Hino |
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Institution: | (1) Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan |
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Abstract: | For conservative symmetric diffusions on a general state space (X,m), the short time asymptotic behavior of tlog
X
1
A
T
t
1
B
dm is investigated, where T
t
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 2 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. |
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Keywords: | short time asymptotics Markovian semigroups intrinsic metric Lyons-Zheng's decomposition walk dimension |
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