A martingale approach to strong convergence in a generalized Pólya- Eggenberger urn model
Consider the following generalized Pólya-Eggenberger urn model: A ball is drawn at random from the urn, its color is noticed and then it is returned to the urn together with A black and B white balls, if a white ball is drawn; and C black and D white balls, otherwise. Let \(T_ n=W_ n+B_ n\) denote the balls contained in the urn at stage n, where \(W_ n\) and \(B_ n\) are the numbers of white and black balls, respectively. The strong convergence for the proportion \(W_ n/T_ n\) is proved by using martingale arguments and under some conditions which are weaker than those in \textit{A. Bagchi} and \textit{A. K. Pal}, SIAM J. Algebraic Discrete Methods 6, 394-405 (1985; Zbl 0568.60010). This result has some applications in the studies of computer data structures.
scientific article; zbMATH DE number 4124700