Hida演算和Malliavin演算中的Levy Laplacian
Levy Laplacians in Hida calculus and Malliavin calculus
摘要：
考虑了随机分析中Levy Laplacian的不同定义之间的某些联系。有两种方法用于定义这些操作符。标准的一个是基于Wiener测度上的Sobolev-Schwartz分布理论（Hida演算）的应用。人们可以考虑链的利维拉普拉斯参数化的一个真正的参数与这种方法的帮助。这个链的一个元素是经典的Levy Laplacian。另一种定义列维拉普拉斯算子的方法是基于维纳测度上的索伯列夫空间理论（Malliavin演算）的应用。证明了在Wiener测度上的Sobolev空间嵌入到Wiener测度上的广义泛函空间时，用第二种方法定义的Levy Laplacian与Levy Laplacian链中的一个元素重合，而这个元素不是经典的Levy Laplacian.证明了随机分析中的Levy-Laplacian与规范场的关系。
英文摘要：
Some connections between different definitions of Levy Laplacians in the stochastic analysis are considered. Two approaches are used to define these operators. The standard one is based on the application of the theory of Sobolev-Schwartz distributions over the Wiener measure (the Hida calculus). One can consider the chain of Levy Laplacians parametrized by a real parameter with the help of this approach. One of the elements of this chain is the classical Levy Laplacian. Another approach to define the Levy Laplacian is based on the application of the theory of Sobolev spaces over the Wiener measure (the Malliavin calculus). It is proved that the Levy Laplacian defined with the help of the second approach coincides with one of the elements of the chain of Levy Laplacians, which is not the classical Levy Laplacian, under the imbedding of the Sobolev space over the Wiener measure into the space of generalized functionals over this measure. It is shown which Levy Laplacian in the stochastic analysis is connected to the gauge fields.
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