On short time asymptotic behavior of some symmetric diffusions on general state spaces
type: Item
instance of: scholarly article
title: On short time asymptotic behavior of some symmetric diffusions on general state spaces
zbMATH Open document ID: 1015.47029
DOI: 10.1023/A:1014033208581
author: Masanori Hino
published in: Potential Analysis
publication date: 2002-05-21T00:00:00Z
review text: The short time behavior of Varadhan's type for heat kernels is considered for a strongly continuous, symmetric Markovian \(L^2\) conservative semigroup on a probability space. In the cases without transition density functions, the lower bound and upper bound of the large deviation rate of transition probability from a set \(A\) to a set \(B\) were given by many authors, such as S. Fang, T. Zhang, S. Aida. In the present paper, the estimation is proven for a general measurable set \(A\) and a set \(B\) in terms of the intrinsic metric. Under some boundedness condition on the associated Dirichlet form, the existence of the corresponding limit for the transition from the set \(A\) to set \(B\) is proven.
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 60H07
zbMATH DE Number: 1742918
zbMATH Keywords: short time asymptotics
zbMATH Keywords: Markovian semigroup
zbMATH Keywords: intrinsic metric
zbMATH Keywords: Lyons Zheng's decomposition
zbMATH Keywords: walk demention
reviewed by: Minping Qian
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1742918