论文标题
与布朗尼的离散近似
Discrete Approximation to Brownian Motion with Darning
论文作者
论文摘要
在[4]和[5，第7章]中介绍并研究了带有围绕的布朗运动（缩写中的BMD）。粗略地说，BMD以无限的速度在“划出区域”上行驶，而其表现就像该区域外的常规BM。在本文中，我们表明，从其状态空间中的一个点开始，BMD是连续时间简单的随机随机步行的弱极限，其正方形晶格的尺寸减小。从其状态空间中的任何顶点，近似随机步行在指数保持时间后以同样的概率跳到其最近的邻居。
Brownian motion with darning (BMD in abbreviation) is introduced and studied in [4] and [5, Chapter 7]. Roughly speaking, BMD travels across the "darning area" at infinite speed, while it behaves like a regular BM outside of this area. In this paper we show that starting from a single point in its state space, BMD is the weak limit of a family of continuous-time simple random walks on square lattices with diminishing mesh sizes. From any vertex in their state spaces, the approximating random walks jump to its nearest neighbors with equal probability after an exponential holding time.
