A martingale approach for Polya urn processes

被引：2
|
作者：
Laulin, Lucile [1 ]
机构：
[1] Univ Bordeaux, Inst Math Bordeaux, UMR 5251, 351 Cours Liberat, F-33405 Talence, France
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2020年 / 25卷
关键词：
Polya urns; martingales; central limit theorem; almost sure convergence; CENTRAL-LIMIT; THEOREMS; CONVERGENCE; LAW;
D O I：
10.1214/20-ECP321
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：
This paper is devoted to a direct martingale approach for Polya urn models asymptotic behaviour. A Polya process is said to be small when the ratio of its replacement matrix eigenvalues is less than or equal to 1/2, otherwise it is called large. We find again some well-known results on the asymptotic behaviour for small and large urn processes. We also provide new almost sure properties for small urn processes.
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页码：1 / 13
页数：13
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