Dirichlet型与右过程的一般对应
A general correspondence between Dirichlet forms and right processes
摘要：
狄利克雷形式理论起源于Beurling-Deny，特别是由Fukushima和Silverstein发展，是经典（和公理化）位势论的自然泛函分析扩展。虽然它的某些部分有抽象的测度论版本，但与Fukushima和Silverstein得到的形式相关联的Hunt过程的基本一般构造要求形式定义在具有Radon测度$m$的局部紧可分空间上，并且形式是正则的（在紧支撑的连续函数在形式的域中是稠密的意义上，在形式和$L^2(m)$ -空间给出的上确界范数和自然范数中）。此设置排除无限维情况。在这封信中，我们宣布，存在着一个扩展的岛-西尔弗斯坦的建设的相关过程的情况下，空间只是应该是度量化和形式不需要是正规的。
英文摘要：
The theory of Dirichlet forms as originated by Beurling-Deny and developed particularly by Fukushima and Silverstein, is a natural functional analytic extension of classical (and axiomatic) potential theory. Although some parts of it have abstract measure theoretic versions, the basic general construction of a Hunt process properly associated with the form, obtained by Fukushima and Silverstein, requires the form to be defined on a locally compact separable space with a Radon measure $m$ and the form to be regular (in the sense of the continuous functions of compact support being dense in the domain of the form, both in the supremum norm and in the natural norm given by the form and the $L^2(m)$-space). This setting excludes infinite dimensional situations. In this letter we announce that there exists an extension of Fukushima-Silverstein's construction of the associated process to the case where the space is only supposed to be metrizable and the form is not required to be regular.
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