On a Class of Markov Semigroups on Discrete Ultra-Metric Spaces

被引：17

作者：

Bendikov, Alexander ^{[2
]}

Grigor'yan, Alexander ^{[1
]}

Pittet, Christophe ^{[3
]}

机构：

[1] Univ Bielefeld, Dept Math, D-33501 Bielefeld, Germany

[2] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland

[3] Univ Aix Marseille 1, CMI, F-13453 Marseille 13, France

来源：

POTENTIAL ANALYSIS | 2012年 / 37卷 / 02期

关键词：

Markov chain; Markov semigroup; Markov generator; Ultra-metric space; Heat kernel; Transition probability; RANDOM-WALKS; DIFFUSION;

D O I：

10.1007/s11118-011-9249-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a discrete ultra-metric space with a measure m and construct in a natural way a symmetric Markov semigroup in and the corresponding Markov process . We prove upper and lower bounds of its transition function and its Green function, give a criterion for the transience, and estimate its moments.

引用

页码：125 / 169

页数：45

共 25 条

[1]

Abramowitz M., 1972, Handbook on Mathematical Functions with Formulas, Graphs, and Mathematical Tables

[2]

BENDIKOV A, 1994, EXPO MATH, V12, P381

[3]

Bendikov A., 2011, MATH ANN IN PRESS

[4]

Bendikov A., 2011, ARXIV11021952V1

[5]

Blumenthal R. M., 1960, Trans. Amer. Math. Soc, V95, P263, DOI [DOI 10.1090/S0002-9947-1960-0119247-6, 10.1090/S0002-9947-1960-0119247-6]

[6] On transience of card shuffling [J].

Brofferio, S ;

Woess, W .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (05) :1513-1519

[7] A geometric approach to on-diagonal heat kernel lower bounds on groups [J].

Coulhon, T ;

Grigor'yan, A ;

Pittet, C .

ANNALES DE L INSTITUT FOURIER, 2001, 51 (06) :1763-+

[8]

Darling D.A., 1962, P AM MATH SOC, V13, P447

[9] Diffusion on locally compact ultrametric spaces [J].

Del Muto, M ;

Figa-Talamanca, A .

EXPOSITIONES MATHEMATICAE, 2004, 22 (03) :197-211

[10] Anisotropic diffusion on totally disconnected abelian groups [J].

Del Muto, Mauro ;

Figa-Talamanca, Alessandro .

PACIFIC JOURNAL OF MATHEMATICS, 2006, 225 (02) :221-229

← 1 2 3 →