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.
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页码：104 / 115
页数：12
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