MARTINGALE FUNCTIONAL CENTRAL LIMIT-THEOREMS FOR A GENERALIZED POLYA URN

• 成果类型: Article
• 署名作者: GOUET, R
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989134
• 发表日期: 1993
• 页码: 1624-1639
• 关键词: model

摘要

In a generalized two-color Polya urn scheme, allowing negative replacements, we use martingale techniques to obtain weak invariance principles for the urn process (W(n)), where W(n) is the number of white balls in the urn at stage n. The normalizing constants and the limiting Gaussian process are shown to depend on the ratio of the eigenvalues of the replacement matrix.