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
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
收藏
页码:409 / 428
页数:20
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