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Mean and variance of balanced Pólya urns

Part of: Limit theorems Combinatorial probability

Published online by Cambridge University Press:  03 December 2020

Svante Janson
Svante Janson*
Affiliation:
Uppsala University
*
*Postal address: Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden. Email: svante.janson@math.uu.se
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Abstract

It is well-known that in a small Pólya urn, i.e., an urn where the second largest real part of an eigenvalue is at most half the largest eigenvalue, the distribution of the numbers of balls of different colours in the urn is asymptotically normal under weak additional conditions. We consider the balanced case, and then give asymptotics of the mean and the covariance matrix, showing that after appropriate normalization, the mean and covariance matrix converge to the mean and covariance matrix of the limiting normal distribution.

Keywords

Pólya urnsmoment convergence

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 60F25: $L^p$-limit theorems
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 4 , December 2020 , pp. 1224 - 1248
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Copyright
© Applied Probability Trust 2020

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