论文标题
Dirichlet形式的非标准表示
Nonstandard Representation of the Dirichlet Form
论文作者
论文摘要
Dirichlet形式是对许多扩散样过程的大量使用Laplacian的概括。在本文中，我们提出了Dirichlet形式的非标准表示定理，表明通常的dirichlet形式可以通过超菲斯总和可以很好地x氧化。这种结果的主要动机之一是提供一种工具，以直接将有关有限或可数状态空间上的dirichlet形式的结果转换为更一般状态空间的结果，而不必翻译证明的详细信息。作为应用程序，我们证明了马尔可夫链在有限状态空间上的众所周知的比较定理的概括，并将我们的结果与以前的概括尝试相关联。
The Dirichlet form is a generalization of the Laplacian, heavily used in the study of many diffusion-like processes. In this paper we present a nonstandard representation theorem for the Dirichlet form, showing that the usual Dirichlet form can be well-approximated by a hyperfinite sum. One of the main motivations for such a result is to provide a tool for directly translating results about Dirichlet forms on finite or countable state spaces to results on more general state spaces, without having to translate the details of the proofs. As an application, we prove a generalization of a well-known comparison theorem for Markov chains on finite state spaces, and also relate our results to previous generalization attempts.
