On regularization of formal Fourier--Wiener transform of the self-intersection local time of planar Gaussian process
On regularization of formal Fourier--Wiener transform of the self-intersection local time of planar Gaussian process
复制标题
平面高斯过程自交局部时间的形式傅立叶--维纳变换的正则化
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Olga L. Izumtseva
中科院分区：
文献类型：
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作者：
A. Dorogovtsev;Olga L. Izumtseva
用对角线发散的积分描述了多个自交局部时间形式表达式的傅里叶-维纳变换。我们在这项工作中使用的正则化方法与具有不可积奇点的函数的正则化有关。考虑了强局部不确定性性质，它比S.Berman提出的局部不确定性性质具有更强的限制性。研究了它在正则化构造中的几何意义。作为例子，解决了平面Wiener过程紧摄动的正则化问题。
Fourier-Wiener transform of the formal expression for multiple self-intersection local time is described in terms of the integral, which is divergent on the diagonals. The method of regularization we use in this work related to regularization of functions with non-integrable singularities. The strong local nondeterminism property, which is more restrictive than the property of local nondeterminism introduced by S.Berman is considered. Its geometrical meaning in the construction of the regularization is investigated. As the example the problem of regularization is solved for the compact perturbation of the planar Wiener process.