Asymptotics for randomly reinforced urns with random barriers
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In this article, the proportion of black balls at time n and 0≤L L is replaced together with a random number Rn of red balls, and under mild conditions it is shown that Zn→a.s.Z for some random variable Z, and Dn≔√n(Zn-Z)→Abstract:
An urn contains black and red balls. Let Zn be the proportion of black balls at time n and 0≤L L, then bn is replaced together with a random number Rn of red balls. Otherwise, no additional balls are added, and bn alone is replaced. In this paper we assume that Rn=Bn. Then, under mild conditions, it is shown that Zn→a.s.Z for some random variable Z, and Dn≔√n(Zn-Z)→read more
Citations
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Networks of reinforced stochastic processes: asymptotics for the empirical means.
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TL;DR: In this article, a new variant of the Eggenberger-polya urn, called the "Rescaled" polya, is introduced, which is characterized by the following features: (i) a local reinforcement mechanism mainly based on the last observations, (ii) a random persistent fluctuation of the predictive mean, and (iii) a long-term convergence of the empirical mean to a deterministic limit.
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TL;DR: In this paper, a new variant of the Eggenberger-polya urn, called the "Rescaled" polya, is introduced, which is characterized by the following features: (i) a local reinforcement mechanism mainly based on the last observations, (ii) a random fluctuation of the conditional probabilities, and (iii) a long-term convergence of the empirical mean to a deterministic limit, together with a chi-squared goodness of fit result.
References
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Journal ArticleDOI
Merging of opinions with increasing information
David Blackwell,Lester E. Dubins +1 more
Book
Polya Urn Models
TL;DR: In this paper, a collection of modern and evolving urn theory and its numerous applications are discussed, including exchangeability, stochastic processes via urns, and functional equations for moment generating functions can be obtained and solved.
Journal ArticleDOI
Asymptotics in randomized urn models
Zhidong Bai,Feifang Hu +1 more
TL;DR: In this article, the authors studied a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1,2,…,n−1.
Journal ArticleDOI
Randomized urn models revisited using Stochastic Approximation
Sophie Laruelle,Gilles Pagès +1 more
TL;DR: In this article, the authors presented the link between stochastic approximation and clinical trials based on randomized urn models investigated in Bai and Hu (1999,2005) and Bai, Hu and Shen (2002).
Journal ArticleDOI
Asymptotics in randomized urn models
Zhidong Bai,Feifang Hu +1 more
TL;DR: In this paper, a very general urn model was studied in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1,2,...,n-1.