A functional limit theorem for lattice oscillating random walks

被引：0

作者：

Tran Duy Vo ^{[1
]}

Peigne, Marc ^{[1
]}

机构：

[1] Univ Tours, CNRS, Inst Denis Poisson, F-37200 Tours, France

来源：

ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS | 2023年 / 20卷 / 02期

关键词：

Oscillating random walk; invariance principle; skew Brownian motion; renewal sequences of operators; Markov chain;

D O I：

10.30757/ALEA.v20-54

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：

This paper is devoted to an invariance principle for Kemperman's model of oscillating random walk on Z. This result appears as an extension of the invariance principal theorem for classical random walks on Z or reflected random walks on N-0. Relying on some natural Markov sub-process which takes into account the oscillation of the random walks between Z(-) and Z(+), we first construct an aperiodic sequence of renewal operators acting on a suitable Banach space and then apply a powerful theorem proved by S. Gouezel.

引用

页码：1433 / 1457

页数：25

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