THE SCALING LIMIT OF SENILE REINFORCED RANDOM WALK

被引：1

作者：

Holmes, Mark ^{[1
]}

机构：

[1] Univ Auckland, Dept Stat, Auckland 1142, New Zealand

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2009年 / 14卷

关键词：

random walk; reinforcement; invariance principle; fractional kinetics; time-change;

D O I：

10.1214/ECP.v14-1449

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：

We prove that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean. We show that under suitable conditions, when T has heavy tails the scaling limit is the so-called fractional kinetics process ,a random time-change of Brownian motion. The proof uses the standard tools of time-change and invariance principles for additive functionals of Markov chains.

引用

页码：104 / 115

页数：12

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