The Annals of Probability

Martingale Functional Central Limit Theorems for a Generalized Polya Urn

Raul Gouet

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Abstract

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.

Article information

Source
Ann. Probab., Volume 21, Number 3 (1993), 1624-1639.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989134

Digital Object Identifier
doi:10.1214/aop/1176989134

Mathematical Reviews number (MathSciNet)
MR1235432

Zentralblatt MATH identifier
0788.60044

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K99: None of the above, but in this section

Keywords
Urn model limit theorems martingales

Citation

Gouet, Raul. Martingale Functional Central Limit Theorems for a Generalized Polya Urn. Ann. Probab. 21 (1993), no. 3, 1624--1639. doi:10.1214/aop/1176989134. https://projecteuclid.org/euclid.aop/1176989134


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