Double Asymptotic for Random Walks on Hypercubes

被引：0

作者：

Montegut, Fabien ^{[1
]}

机构：

[1] Univ Toulouse, CNRS, UMR5219, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse 9, France

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2019年 / 32卷 / 04期

关键词：

Limit theorems; Markov chains; Hypercube;

D O I：

10.1007/s10959-019-00931-y

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 consider the sum of the coordinates of a simple random walk on the K-dimensional hypercube and prove a double asymptotic of this process, as both the time parameter n and the space parameter K tend to infinity. Depending on the asymptotic ratio of the two parameters, the rescaled processes converge toward either a "stationary Brownian motion," an Ornstein-Uhlenbeck process or a Gaussian white noise.

引用

页码：2044 / 2065

页数：22

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