Stochastic Analysis on Product Manifolds: Dirichlet Operators on Differential Forms
Stochastic Analysis on Product Manifolds: Dirichlet Operators on Differential Forms
复制标题
乘积流形的随机分析：微分形式的狄利克雷算子
DOI：
10.1006/jfan.2000.3629
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发表时间：
2000
影响因子：
1.7
通讯作者：
Y. Kondratiev
中科院分区：
文献类型：
--
作者：
S. Albeverio;A. Daletskii;Y. Kondratiev
摘要我们定义了乘积流形（紧致流形的无穷乘积）上的de Rham复形，以及微分形式上的Dirichlet算子，与可微测度（特别是Gibbs测度）相关联，推广了Bochner和de Rham Laplacian的概念。给出了相应半群的概率表示，并研究了相应随机动力学的性质。
Abstract We define a de Rham complex over a product manifold (infinite product of compact manifolds), and Dirichlet operators on differential forms, associated with differentiable measures (in particular, Gibbs measures), which generalize the notions of Bochner and de Rham Laplacians. We give probabilistic representations for corresponding semigroups and study properties of the corresponding stochastic dynamics.