Martin boundary of a killed random walk on a half-space

被引：16

作者：

Ignatiouk-Robert, Irina ^{[1
]}

机构：

[1] Univ Cergy Pontoise, Dept Math, F-95302 Cergy Pontoise, France

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2008年 / 21卷 / 01期

关键词：

Martin boundary; sample path large deviations; random walk;

D O I：

10.1007/s10959-007-0100-3

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：

A complete representation of the Martin boundary of killed random walks on a half-space Z(d-1) x N-* is obtained. In particular, it is proved that the corresponding Martin boundary is homemorphic to the half-sphere S-+(d) = {z epsilon Rd-1 x R+ :vertical bar z vertical bar = 1}. The method is based on a combination of ratio limits theorems and large deviation techniques.

引用

页码：35 / 68

页数：34

共 24 条

[1] Martin boundaries associated with a killed random walk [J].

Alili, L ;

Doney, RA .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2001, 37 (03) :313-338

[2]

[Anonymous], 2011, APPL MATH

[3]

[Anonymous], 1969, RUSS MATH SURV+

[4]

[Anonymous], REAL COMPLEX ANAL

[5]

BILLINGSLEY P, 1968, WILEY SERIES PROBAIL

[6]

BOROVKOV AA, 1992, SIBERIAN MATH J, V33, P745

[7]

CARTIER P, 1972, S MATH, V9, P203

[8] An elementary proof of the local central limit theorem [J].

Davis, B ;

McDonald, D .

JOURNAL OF THEORETICAL PROBABILITY, 1995, 8 (03) :693-701

[9] The Martin boundary and ratio limit theorems for killed random walks [J].

Doney, RA .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1998, 58 :761-768

[10]

DOOB JL, 1959, J MATH MECH, V8, P433

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