Dirichlet Operators via Stochastic Analysis
Dirichlet Operators via Stochastic Analysis
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DOI：
10.1006/jfan.1995.1025
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发表时间：
1995-02
影响因子：
1.7
通讯作者：
S. Albeverio;Y. Kondratiev;M. Röckner
中科院分区：
文献类型：
--
作者：
S. Albeverio;Y. Kondratiev;M. Röckner
本文给出了Hilbert空间上由概率测度给出的与经典Dirichlet型相关的对称微分算子（Dirichlet算子）的本质自伴性的充分条件.在对测度作对数正态分布的附加假设下，证明了Dirichlet算子的谱下端存在一个缺口，并证明了相应半群的遍历性.我们也考虑应用到一些经典的晶格系统中的随机动力学的研究。
Abstract We give sufficient conditions for essential self-adjointness of symmetric differential operators (Dirichlet operators) associated with classical Dirichlet forms given by probability measures on Hilbert spaces. Under an additional assumption of log-concavity for the measures we prove the existence of a gap at the lower end of spectrum of the Dirichlet operator and the ergodicity of the corresponding semi-group. We consider also applications to the study of stochastic dynamics in some classical lattice systems.