广义多维受激随机漫步的瞬态说明

Pub Date : 2024-01-11 DOI:10.1007/s10959-023-01311-3

Rodrigo B. Alves, Giulio Iacobelli, Glauco Valle

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引用次数: 0

摘要

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。

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

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

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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