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- Title
On a class of random walks in simplexes.
- Authors
Nguyen, Tuan-Minh; Volkov, Stanislav
- Abstract
We study the limit behaviour of a class of random walk models taking values in the standard d-dimensional ( $d\ge 1$) 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.
- Publication
Journal of Applied Probability, 2020, Vol 57, Issue 2, p409
- ISSN
0021-9002
- Publication type
Article
- DOI
10.1017/jpr.2020.19