In this paper, we look at a probabilistic approach to a non-local quadratic form that has lately attracted some interest. This form is related to a recently introduced non-local normal derivative. The goal is to construct two Markov process: one corresponding to that form and the other which is related to a probabilistic interpretation of the Neuman problem. We also study the Dirichlet-to-Neumann operator for non-local operators.

中文翻译：

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非局部二次型的概率方法及其与 Neumann 边界条件问题的联系

在本文中，我们研究了一种最近引起一些兴趣的非局部二次型的概率方法。这种形式与最近引入的非局部正态导数有关。目标是构建两个马尔可夫过程：一个对应于该形式，另一个与诺依曼问题的概率解释相关。我们还研究了非局部算子的 Dirichlet-to-Neumann 算子。