This note concerns the distribution of Skew Brownian motion with dry friction and its occupation time. These distributions were obtained in Berezin and Zayats (2019) by using the Laplace transform and joint characteristic functions. We provide an alternative approach, which is based on the use of the joint density for Skew Brownian motion, its last visit to the origin, its local and occupation times derived in Gairat and Shcherbakov (2017).

中文翻译：

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具有干摩擦的斜布朗运动：联合密度方法

本说明涉及带有干摩擦的斜布朗运动的分布及其占用时间。这些分布是在 Berezin 和 Zayats (2019) 中通过使用拉普拉斯变换和联合特征函数获得的。我们提供了一种替代方法，该方法基于使用斜布朗运动的联合密度、对原点的最后一次访问、在 Gairat 和 Shcherbakov (2017) 中得出的局部和占用时间。