On the asymptotic behavior of the Diaconis–Freedman chain in a multi-dimensional simplex

Autor:	Marc Peigné, Tat Dat Tran
Rok vydání:	2022
Předmět:	Statistics and Probability General Mathematics Statistics Probability and Uncertainty
Zdroj:	Journal of Applied Probability. 59:505-526
ISSN:	1475-6072 0021-9002
DOI:	10.1017/jpr.2021.64
Popis:	We give a setting of the Diaconis–Freedman chain in a multi-dimensional simplex and consider its asymptotic behavior. By using techniques from random iterated function theory and quasi-compact operator theory, we first give some sufficient conditions which ensure the existence and uniqueness of an invariant probability measure and, in particular cases, explicit formulas for the invariant probability density. Moreover, we completely classify all behaviors of this chain in dimension two. Some other settings of the chain are also discussed.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7c5b66cb7a7303ecabfdf72b481765dd https://doi.org/10.1017/jpr.2021.64 Zobrazit plný text záznamu