Limit theorems for triangular urn schemes |
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Authors: | Svante Janson |
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Institution: | (1) Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden |
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Abstract: | We study a generalized Pólya urn with balls of two colours and a triangular replacement matrix; the urn is not required to
be balanced. We prove limit theorems describing the asymptotic distribution of the composition of the urn after a long time.
Several different types of asymptotics appear, depending on the ratio of the diagonal elements in the replacement matrix;
the limit laws include normal, stable and Mittag-Leffler distributions as well as some less familiar ones. The results are
in some cases similar to, but in other cases strikingly different from, the results for irreducible replacement matrices. |
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Keywords: | |
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