An intuitive approach to the Martin boundary

被引:3
作者
Loeb, Peter A. [1 ]
机构
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
来源
INDAGATIONES MATHEMATICAE-NEW SERIES | 2020年 / 31卷 / 05期
关键词
Martin boundary; Nonstandard analysis; Representing measures; NONSTANDARD;
D O I
10.1016/j.indag.2020.01.009
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
An intuitive probabilistic alternative for the construction of the Martin boundary is presented along with a construction of maximal representing measures for positive harmonic functions. (C) 2020 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码:879 / 884
页数:6
相关论文
共 14 条
[1]   NONSTANDARD REPRESENTATION FOR BROWNIAN-MOTION AND ITO INTEGRATION [J].
ANDERSON, RM .
ISRAEL JOURNAL OF MATHEMATICS, 1976, 25 (1-2) :15-46
[2]  
[Anonymous], 2016, Real Analysis
[3]  
Brelot M, 1971, LECT NOTES MATH, V175
[4]  
Doob J., 1984, GRUNDLEHREN MATH WIS
[5]  
Fuchssteiner B., 1974, Journal of Functional Analysis, V16, P1, DOI 10.1016/0022-1236(74)90068-8
[6]   POSITIVE HARMONIC FUNCTIONS ON LIPSCHITZ DOMAINS [J].
HUNT, RA ;
WHEEDEN, RL .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 147 (02) :507-&
[7]  
Insall M., HAUSDORFF COMP UNPUB
[8]   End Compactifications and General Compactifications [J].
Insall, Matt ;
Loeb, Peter A. ;
Marciniak, Malgorzata Aneta .
JOURNAL OF LOGIC AND ANALYSIS, 2014, 6
[9]   CONVERSION FROM NONSTANDARD TO STANDARD MEASURE SPACES AND APPLICATIONS IN PROBABILITY THEORY [J].
LOEB, PA .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 211 (OCT) :113-122
[10]   APPLICATIONS OF NONSTANDARD ANALYSIS TO IDEAL BOUNDARIES IN POTENTIAL THEORY [J].
LOEB, PA .
ISRAEL JOURNAL OF MATHEMATICS, 1976, 25 (1-2) :154-187