Journal of Applied Probability

Strong convergence for urn models with reducible replacement policy

R. Abraham, J. S. Dhersin, and B. Ycart

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A multitype urn scheme with random replacements is considered. Each time a ball is picked, another ball is added, and its type is chosen according to the transition probabilities of a reducible Markov chain. The vector of frequencies is shown to converge almost surely to a random element of the set of stationary measures of the Markov chain. Its probability distribution is characterized as the solution to a fixed point problem. It is proved to be Dirichlet in the particular case of a single transient state to which no return is possible. This is no longer the case, however, as soon as returns to transient states are allowed.

Article information

J. Appl. Probab. Volume 44, Number 3 (2007), 652-660.

First available in Project Euclid: 13 September 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F15: Strong theorems

Urn model Markov chain strong convergence


Abraham, R.; Dhersin, J. S.; Ycart, B. Strong convergence for urn models with reducible replacement policy. J. Appl. Probab. 44 (2007), no. 3, 652--660. doi:10.1239/jap/1189717535.

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