Sierpinski gasket as a Martin boundary I: Martin kernels - Dedicated to Professor Masatoshi Fukushima on the occasion of his 60th birthday

被引：26
作者：
Denker, M
Sato, H
机构：
[1] Univ Gottingen, Inst Math Stochast, D-37083 Gottingen, Germany
[2] Kyushu Univ, Grad Sch Math, Fukuoka 81281, Japan
来源：
POTENTIAL ANALYSIS | 2001年 / 14卷 / 03期
关键词：
Martin boundary; Sierpinski gasket; Markov chain;
D O I：
10.1023/A:1011232724842
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that a Sierpinski gasket in N dimension is homeomorphic to the minimal Martin boundary of some canonical Markov chain. This provides a new class of examples for the boundary theory of Markov chains and the basis for a harmonic analysis on p.c.f. fractal structures.
引用
收藏
页码：211 / 232
页数：22
相关论文
共 16 条
  • [1] ANCONA A, 1988, LECT NOTES MATH, V1344, P1
  • [2] [Anonymous], 1969, RUSS MATH SURV+
  • [3] BROWNIAN-MOTION ON THE SIERPINSKI GASKET
    BARLOW, MT
    PERKINS, EA
    [J]. PROBABILITY THEORY AND RELATED FIELDS, 1988, 79 (04) : 543 - 623
  • [4] CARTIER P, 1972, S MATH, V9, P203
  • [5] CARTWRIGHT DI, 1991, J THEORET PROBAB, V4, P111
  • [6] DOOB JL, 1959, J MATH MECH, V8, P433
  • [7] DYNKIN EB, 1961, SOV MATH DOKL, V2, P399
  • [8] Goldstein S., 1987, RANDOM WALKS DIFFUSI
  • [9] GROMOV M, 1987, MATH SCI RES I PUBL, V9, P75
  • [10] RANDOM-WALKS ON DISCRETE-GROUPS - BOUNDARY AND ENTROPY
    KAIMANOVICH, VA
    VERSHIK, AM
    [J]. ANNALS OF PROBABILITY, 1983, 11 (03) : 457 - 490
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