Probability Theory and Related Fields

, Volume 134, Issue 3, pp 417–452 | Cite as

Limit theorems for triangular urn schemes

  • Svante JansonEmail author


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.


Black Ball Characteristic Function Limit Theorem Asymptotic Normality Probability Generate Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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