Strong convergence for urn models with reducible replacement policy

Abstract : 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 more the case as soon as returns to transient states are allowed.
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Submitted on : Thursday, July 20, 2006 - 6:00:08 PM
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Romain Abraham, Jean-Stephane Dhersin, Bernard Ycart. Strong convergence for urn models with reducible replacement policy. Journal of Applied Probability, Applied Probability Trust, 2007, 44 (3), pp.652-660. ⟨10.1239/jap/1189717535⟩. ⟨hal-00087017⟩

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