In this paper, we study the joint Laplace transform of the sticky Brownian motion on an interval, its occupation time at zero and its integrated process. The perturbation approach of Li and Zhou [The joint Laplace transforms for diffusion occupation times, Adv. Appl. Probab. 45 (2013) 1049–1067] is adopted to convert the problem into the computation of three Laplace transforms, which is essentially equivalent to solving the associated differential equations with boundary conditions. We obtain the explicit expression for the joint Laplace transform in terms of the modified Bessel function and Airy functions.

中文翻译：

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与区间上的粘性布朗运动相关的拉普拉斯变换的结果

在本文中，我们研究了粘性布朗运动在一个区间上的联合拉普拉斯变换，它的零占用时间及其积分过程。Li 和 Zhou 的摄动方法 [扩散占据时间的联合拉普拉斯变换，进阶。应用程序。概率。 45(2013) 1049-1067] 被采用将问题转化为三个拉普拉斯变换的计算，这本质上等同于求解具有边界条件的相关微分方程。我们根据修正的贝塞尔函数和艾里函数获得联合拉普拉斯变换的显式表达式。