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.
Citation
Raul Gouet. "Martingale Functional Central Limit Theorems for a Generalized Polya Urn." Ann. Probab. 21 (3) 1624 - 1639, July, 1993. https://doi.org/10.1214/aop/1176989134
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