Asymptotics and spectral results for random walks on p-adics

被引：27

作者：

Albeverio, S ^{[1
]}

Karwowski, W

Zhao, XL

机构：

[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

[2] SFB 237, Essen, Germany

[3] SFB 237, Bochum, Germany

[4] SFB 237, Dusseldorf, Germany

[5] SFB 256, Bonn, Germany

[6] BiBoS Res Ctr, D-33615 Bielefeld, Germany

[7] CERFIM, Locarno, Switzerland

[8] Univ Wroclaw, Inst Theoret Phys, PL-50138 Wroclaw, Poland

[9] Shantou Univ, Inst Math, Shantou 515063, Peoples R China

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1999年 / 83卷 / 01期

基金：

美国国家科学基金会;

关键词：

Markov processes on p-adic space; null recurrence; spectral properties of a generator on p-adic space; Dirichlet forms; jump processes;

D O I：

10.1016/S0304-4149(99)00016-2

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：

Markov semigroups on the field Q(p) of p-adic numbers which are symmetric with respect to a measure p(x) dx absolutely continuous relative to the Haar measure dx on Q(p) are constructed. The corresponding Dirichlet forms and associated Markov processes are exhibited and shown to be of the jump type. A detailed description of the spectrum of the generator (eigenvalues and eigenfunctions) is provided. Necessary and sufficient conditions for reducibility, recurrence and transience are found. Results about exit times from balls are also presented, as well as a proof of null recurrence. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：39 / 59

页数：21

共 40 条

[1] A RANDOM-WALK ON P-ADICS - THE GENERATOR AND ITS SPECTRUM [J].

ALBEVERIO, S ;

KARWOWSKI, W .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1994, 53 (01) :1-22

[2]

ALBEVERIO S, 1991, S PROB STAT, V1, P86

[3]

ALBEVERIO S, 1985, STOCHASTIC DIFFERENT, P1

[4]

[Anonymous], J THEOR PROBAB, DOI 10.1007/BF01049177

[5]

[Anonymous], SEM STOCH PROC 1988

[6]

BLUMENTHAL RM, 1968, MARKOV PROCESSES POT

[7]

BREKKE L, 1989, P ADIC DIFFUSION REL

[8]

Cartier P., 1973, P S PURE MATH, V26, P419

[9]

DWORK B, 1982, LECT P ADIC DIFFEREN

[10]

ETHIER S., 1986, MARKOV PROCESSES CHA, DOI 10.1002/9780470316658

← 1 2 3 4 →