论文标题
布朗时零自我交流零的渐近学的改进
Refinements of asymptotics at zero of Brownian self-intersection local times
论文作者
论文摘要
在本文中，我们建立了一些与高斯密度和Hermite多项式有关的估计，以便获得对布朗尼运动本地自我交流的每个术语几乎确定的估计。在维度$ d \ geqslant 4 $中，布朗运动的当地时代可以被视为经典维也纳空间上的一系列措施。我们提供了一些相对于这些措施的渐近学。最后，我们试图估计这些措施与维纳措施之间的二次瓦斯汀距离。
In this article we establish some estimates related to the Gaussian densities and to Hermite polynomials in order to obtain an almost sure estimate for each term of the Itô-Wiener expansion of the self-intersection local times of the Brownian motion. In dimension $d\geqslant 4$ the self-intersection local times of the Brownian motion can be considered as a family of measures on the classical Wiener space. We provide some asymptotics relative to these measures. Finally, we try to estimate the quadratic Wasserstein distance between these measures and the Wiener measure.
