Finite-memory elephant random walk and the central limit theorem

被引：0

作者：

Ben-Ari, Iddo ^{[1
]}

Green, Jonah ^{[2
]}

Meredith, Taylor ^{[3
]}

Panzo, Hugo ^{[4
]}

Tan, Xioran ^{[1
]}

机构：

[1] Univ Connecticut, Storrs, CT 06269 USA

[2] CUNY, Lehman Coll, Bronx, NY 10468 USA

[3] NYU, 550 1St Ave, New York, NY 10012 USA

[4] Technion Israel Inst Technol, IL-32000 Haifa, Israel

来源：

BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS | 2021年 / 35卷 / 02期

关键词：

Key words and phrases; Central limit theorem; additive functional; finite-state Markov chain; elephant random walk;

D O I：

10.1214/20-BJPS475

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：

The Central Limit Theorem (CLT) for additive functionals of Markov chains is a well-known result with a long history. In this paper, we present applications to two finite-memory versions of the Elephant Random Walk, solving a problem from Gut and Stadtm?eller (2018). We also present a derivation of the CLT for additive functionals of finite state Markov chains, which is based on positive recurrence, the CLT for IID sequences and some elementary linear algebra, and which focuses on characterization of the variance.

引用

页码：242 / 262

页数：21

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