## The Annals of Probability

### Martingale Functional Central Limit Theorems for a Generalized Polya Urn

Raul Gouet

#### 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

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