有界域内变维布朗运动的离散逼近

IF 0.5 4区数学 Q3 MATHEMATICS

Kyoto Journal of Mathematics Pub Date : 2023-08-01 DOI:10.1215/21562261-10607383

Shuwen Lou

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引用次数: 0

摘要

在本文中，我们研究了Chen和Lou在他们2019年的论文中引入的具有正方形格上连续时间随机行走的布朗运动(BMVD)的离散近似。BMVD的状态空间包含一个二维分量、一个三维分量和一个连接这两个分量的“织补点”。这种状态空间具有测地线距离，在测地线距离下BMVD是一个扩散过程。本文证明了限制在包含织补点的有界域上的BMVD是指数保持时间连续可逆随机漫步的弱极限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Discrete approximation to Brownian motion with varying dimension in bounded domains

In this paper, we study a discrete approximation to Brownian motion with varying dimension (BMVD) introduced by Chen and Lou in their 2019 paper with continuous time random walks on square lattices. The state space of BMVD contains a 2-dimensional component, a 3-dimensional component, and a “darning point” which joins these two components. Such a state space is equipped with the geodesic distance under which BMVD is a diffusion process. In this paper, we prove that BMVD restricted on a bounded domain containing the darning point is the weak limit of continuous-time reversible random walks with exponential holding times.

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来源期刊

Kyoto Journal of Mathematics MATHEMATICS-

CiteScore

1.10

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyoto Journal of Mathematics publishes original research papers at the forefront of pure mathematics, including surveys that contribute to advances in pure mathematics.