论文标题
扩散蜘蛛：绿色内核，过多的功能和最佳停止
Diffusion spiders: Green kernel, excessive functions and optimal stopping
论文作者
论文摘要
扩散蜘蛛是一个强大的马尔可夫过程，其连续路径在一个顶点和一个有限数量的边缘（无限长度）上占据图。沃尔什（Walsh）的布朗蜘蛛（Brownian Spider）就是一个例子，每个边缘上的过程都表现为布朗运动。我们根据潜在扩散的特性来计算分解核的密度。通过马丁边界理论研究了过多的功能。主要结果是代表给定过多功能的度量的明确表达式。这些结果用于解决扩散蜘蛛的最佳停止问题。
A diffusion spider is a strong Markov process with continuous paths taking values on a graph with one vertex and a finite number of edges (of infinite length). An example is Walsh's Brownian spider where the process on each edge behaves as Brownian motion. We calculate the density of the resolvent kernel in terms of the characteristics of the underlying diffusion. Excessive functions are studied via the Martin boundary theory. The main result is an explicit expression for the representing measure of a given excessive function. These results are used to solve optimal stopping problems for diffusion spiders.
