论文标题
非本地边界价值问题，随机重置和图表上的布朗动作
Non-local Boundary Value Problems, stochastic resetting and Brownian motions on graphs
论文作者
论文摘要
我们考虑涉及非本地操作员的动态边界条件。我们的分析包括对此类运营商的详细描述以及与随机时间和随机（加法）功能的关系。我们根据非本地运算符和边界价值问题之间的相互作用为布朗运动的边界行为提供了一些新的特征。我们的主要重点是Feller-Wentzell扩散。我们首先考虑真实行的启发性案例，然后将结果扩展到带有诱捕点或排斥顶点的星形图上。
We consider dynamic boundary conditions involving non-local operators. Our analysis includes a detailed description of such operators together with their relations with random times and random (additive) functionals. We provide some new characterizations for the boundary behaviour of the Brownian motion based on the interplay between non-local operators and boundary value problems. Our main focus is on Feller-Wentzell diffusions. We first consider the instructive case of the real line, then we extend our results on star graphs with trapping points or repulsive vertices.
