A Note on Transience of Generalized Multi-Dimensional Excited Random Walks

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability Pub Date : 2024-01-11 DOI:10.1007/s10959-023-01311-3

Rodrigo B. Alves, Giulio Iacobelli, Glauco Valle

引用次数: 0

Abstract

We consider a variant of the generalized excited random walk (GERW) in dimension \(d\ge 2\) where the lower bound on the drift for excited jumps is time-dependent and decays to zero. We show that if the lower bound decays more slowly than \(n^{-\beta _0}\) (n is time), where \(\beta _0\) depends on the transitions of the process, the GERW is transient in the direction of the drift.

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广义多维受激随机漫步的瞬态说明

我们考虑了广义激发随机游走（GERW）在维度（d\ge 2\）上的一个变体，在这个变体中，激发跳跃的漂移下限是随时间变化的，并且会衰减为零。我们证明，如果下限的衰减速度慢于\(n^{-\beta _0}\)（n是时间），其中\(\beta _0\)取决于过程的转换，那么GERW在漂移方向上就是瞬态的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Theoretical Probability 数学-统计学与概率论

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.