Local times of self-intersection for multidimensional Brownian motion
Local times of self-intersection for multidimensional Brownian motion
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DOI：
10.1017/s0027763000005183
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发表时间：
1995-06
影响因子：
0.8
通讯作者：
S. He;W. Yang;Rong-Qin Yao;Jia-gang Wang
中科院分区：
文献类型：
--
作者：
S. He;W. Yang;Rong-Qin Yao;Jia-gang Wang
在白色噪声分析的框架下，我们将定义多维布朗运动的局部自相交时为广义维纳泛函。Watanabe（[6]）.利用函数的混沌表示和精确计算，我们对这一问题有了更深入的认识。第一节给出了多维布朗运动的多重Wiener积分和平方可积Wiener泛函的混沌表示。它们是必不可少的，但似乎没有被明确和正确地制定之前。白色噪声分析的有用概念和结果在第2节中说明。第三部分是本文的主体部分。第四节简要介绍了其在本地时间中的应用。
We will define local times of self-intersection for multidimensional Brownian motion as generalized Wiener functionals under the framework of white noise analysis as in H. Watanabe ([6]). By making use of the chaotic representation of -function and precise computation we get a deep insight into the problem. In the section 1 multiple Wiener integrals with respect to multidimensional Brownian motion and chaotic representations for square-integrable Wiener functionals are given. They are indispensable, but seem not to be formulated clearly and correctly before. The useful concepts and results of white noise analysis are illustrated in the section 2. Section 3 is the main part of the paper. The applications to local times are introduced in the section 4 briefly.