Wiener sausage and self-intersection local times
Wiener sausage and self-intersection local times
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DOI：
10.1016/0022-1236(90)90108-w
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发表时间：
1990-02
影响因子：
1.7
通讯作者：
J. Gall
中科院分区：
文献类型：
--
作者：
J. Gall
设B=（Bt，t <$0）是R2中的标准布朗运动.对任意ε> 0和R2的任意紧子集K，定义与K相关的半径为ε的Wiener香肠为集合B + εK，s <$[0，1]的并.本文给出了当半径ε趋于0时，Wiener香肠面积的完全渐近展开式。展开式的第k项的阶数为<$log ε <$− k，并且包含一个随机变量，该随机变量测量过程的k重自相交的数目。这种随机变量被称为（重正化）自相交局部时，最近由EB Dynkin引入和研究。一个自包含的建设，这些地方的时间，连同一些新的近似。
Let B=(B t, t⩾ 0) be a standard Brownian motion in R 2. For every ε> 0 and every compact subset K of R 2, the Wiener sausage of radius ε associated with K is defined as the union of the sets B s+ εK, s ϵ [0, 1]. The present paper gives full asymptotic expansions for the area of the Wiener sausage, when the radius ε goes to 0. The kth term of the expansion is of order¦ log ε¦− k and involves a random variable which measures the number of k-multiple self-intersections of the process. Such random variables are called (renormalized) self-intersection local times and have been recently introduced and studied by EB Dynkin. A self-contained construction of these local times is given, together with a number of new approximations.