In this paper, we study the self-intersection local times of multifractional Brownian motion (mBm) in higher dimensions in the framework of white noise analysis. We show that when a suitable number of kernel functions of self-intersection local times of mBm are truncated then we obtain a Hida distribution. In addition, we present the expansion of the self-intersection local times in terms of Wick powers of white noises. Moreover, we obtain the convergence of the regularized truncated self-intersection local times in the sense of Hida distributions.

中文翻译：

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高维多分数布朗运动的自相交局部时间：一种白噪声方法

在本文中，我们在白噪声分析的框架下研究了高维多分数布朗运动（mBm）的自相交局部时间。我们表明，当适当数量的 mBm 的自相交本地时间的核函数被截断时，我们获得了 Hida 分布。此外，我们根据白噪声的 Wick 幂提出了自相交局部时间的扩展。此外，我们获得了Hida分布意义上的正则化截断自相交局部时间的收敛性。