On a class of random walks in simplexes
Nguyen, Tuan Minh LU and Volkov, Stanislav LU
(2020)
In Journal of Applied Probability
57(2).
p.409-428
- Abstract
We study the limit behaviour of a class of random walk models taking values in the standard d-dimensional simplex. From an interior point z, the process chooses one of the 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/b429aebd-7da7-4689-9980-22fbd3c567a9
- author
- Nguyen, Tuan Minh
LU
and Volkov, Stanislav
LU
- organization
- publishing date
- 2020
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Dirichlet distribution, iterated random functions, Keywords: Random walks in simplexes, stick-breaking process
- in
- Journal of Applied Probability
- volume
- 57
- issue
- 2
- pages
- 20 pages
- publisher
- Applied Probability Trust
- external identifiers
-
- scopus:85089349801
- ISSN
- 0021-9002
- DOI
- 10.1017/jpr.2020.19
- language
- English
- LU publication?
- yes
- id
- b429aebd-7da7-4689-9980-22fbd3c567a9
- date added to LUP
- 2020-08-24 07:22:53
- date last changed
- 2022-04-19 00:23:37
@article{b429aebd-7da7-4689-9980-22fbd3c567a9,
abstract = {{<p>We study the limit behaviour of a class of random walk models taking values in the standard d-dimensional simplex. From an interior point z, the process chooses one of the 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. </p>}},
author = {{Nguyen, Tuan Minh and Volkov, Stanislav}},
issn = {{0021-9002}},
keywords = {{Dirichlet distribution; iterated random functions; Keywords: Random walks in simplexes; stick-breaking process}},
language = {{eng}},
number = {{2}},
pages = {{409--428}},
publisher = {{Applied Probability Trust}},
series = {{Journal of Applied Probability}},
title = {{On a class of random walks in simplexes}},
url = {{http://dx.doi.org/10.1017/jpr.2020.19}},
doi = {{10.1017/jpr.2020.19}},
volume = {{57}},
year = {{2020}},
}