In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval (0,1) with boundary conditions which relate first and second spatial derivatives at the boundary points. Moreover, the unique solution to this problem can be represented probabilistically in terms of a sticky Brownian motion. This probabilistic representation is attained from the stochastic differential equation for a sticky Brownian motion on the bounded interval [0,1].

中文翻译：

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粘性布朗运动和两点边值问题的概率解

在本文中，我们研究了一个两点边界值问题，该问题由开放区间（0,1）上的热方程组成，边界条件与边界点的一阶和二阶空间导数相关。此外，可以通过粘性布朗运动来概率表示该问题的唯一解决方案。该概率表示是从有界区间[0,1]上的粘性布朗运动的随机微分方程获得的。