ON A CLASS OF RANDOM WALKS IN SIMPLEXES

被引：3

作者：

Nguyen, Tuan-Minh ^{[1
]}

Volkov, Stanislav ^{[2
]}

机构：

[1] Monash Univ, Sch Math Sci, Clayton, Vic 3800, Australia

[2] Lund Univ, Ctr Math Sci, S-22100118 Lund, Sweden

来源：

JOURNAL OF APPLIED PROBABILITY | 2020年 / 57卷 / 02期

基金：

瑞典研究理事会;

关键词：

Random walks in simplexes; iterated random functions; Dirichlet distribution; stick-breaking process; DIRICHLET;

D O I：

10.1017/jpr.2020.19

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 study the limit behaviour of a class of random walk models taking values in the standard d-dimensional (d >= 1) simplex. From an interior point z, the process chooses one of the d + 1 vertices of the simplex, with probabilities depending on z, and then the particle randomly jumps to a new location z' on the segment connecting z to the chosen vertex. In some special cases, using properties of the Beta distribution, we prove that the limiting distributions of the Markov chain are Dirichlet. We also consider a related history-dependent random walk model in [0, 1] based on an urn-type scheme. We show that this random walk converges in distribution to an arcsine random variable.

引用

页码：409 / 428

页数：20

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