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A new urn model. (English) Zbl 1093.60007
From the authors’ summary: A single urn contains \(b\) black balls and \(w\) white balls. For each observation, we randomly draw \(m\) balls and note their colors, say \(k\) black balls and \(m-k\) white balls. We return the drawn balls to the urn with additional \(ck\) black balls and \(c(m-k)\) white balls. This procedure is repeated \(n\) times and let \(X_n\) be the fraction of black balls after the \(n\)th draw. The asymptotic properties of \(X_n\) are investigated and it is shown that \((X_n)\) is a martingale which converges a.s. to a r.v. \(X\) whose distribution is absolutely continuous.

60C05 Combinatorial probability
60G42 Martingales with discrete parameter
60F15 Strong limit theorems
Full Text: DOI
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