One-point reflection

被引：15

作者：

Chen, Zhen-Qing ^{[1
]}

Fukushima, Masatoshi ^{[2
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Osaka Univ, Branch Math Sci, Toyonaka, Osaka 5600043, Japan

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 04期

基金：

美国国家科学基金会;

关键词：

Boundary theory; One-point reflection; Excursion law; Local time; Dirichlet form; Brownian motion with darning; Conformal invariance; Harmonic functions; MARKOV-PROCESSES; BOUNDARY-CONDITIONS; BROWNIAN-MOTION; WEAK DUALITY; EXTENSIONS; DIFFUSIONS; EXCURSIONS;

D O I：

10.1016/j.spa.2014.11.002

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We examine symmetric extensions of symmetric Markov processes with one boundary point. Relationship among various normalizations of local times, entrance laws and excursion laws is studied. Dirichlet form characterization of elastic one-point reflection of symmetric Markov processes is derived. We give a direct construction of Walsh's Brownian motion as a one-point reflection together with its Dirichlet form characterization. This yields directly the analytic characterization of harmonic and subharmonic functions for Walsh's Brownian motion, recently obtained by Fitzsimmons and Kuter (2014) using a different method. We further study as a one-point reflection two-dimensional Brownian motion with darning (BMD). (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：1368 / 1393

页数：26

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