In this paper, 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 $d\ge 4$ 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.

中文翻译：

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布朗自交局部时间为零处渐近的改进

在本文中，我们建立了一些与高斯密度和埃尔米特多项式相关的估计，以便获得布朗运动自相交局部时间的伊藤-维纳展开的每一项几乎确定的估计。在维度上$d\ge 4$布朗运动的自交局部时间可以被视为经典维纳空间上的一系列测度。我们提供了一些与这些措施相关的渐近函数。最后，我们尝试估计这些测度与维纳测度之间的二次 Wasserstein 距离。