Urn models

1994 ◽  
pp. 133-145
Author(s):  
Gunnar Blom ◽  
Lars Holst ◽  
Dennis Sandell
Keyword(s):  
Urn Models

Ehrenfest urn models

1965 ◽  
Vol 2 (02) ◽  
pp. 352-376 ◽  
Author(s):  
Samuel Karlin ◽  
James McGregor
Keyword(s):  
Exponential Distribution ◽  
Continuous Time ◽  
Random Variables ◽  
Independent Random Variables ◽  
Urn Models ◽  
Time Intervals ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Random Times

In the Ehrenfest model with continuous time one considers two urns and N balls distributed in the urns. The system is said to be in stateiif there areiballs in urn I, N −iballs in urn II. Events occur at random times and the time intervals T between successive events are independent random variables all with the same negative exponential distributionWhen an event occurs a ball is chosen at random (each of theNballs has probability 1/Nto be chosen), removed from its urn, and then placed in urn I with probabilityp, in urn II with probabilityq= 1 −p, (0 <p< 1).

Some limit theorems in urn models with indistinguishable balls

1988 ◽  
Vol 1988 (1-3) ◽  
pp. 117-123 ◽  
Author(s):  
N. K. Indira ◽  
V. V. Menon
Keyword(s):  
Limit Theorems ◽  
Urn Models

scholarly journals Asymptotic Properties of Multicolor Randomly Reinforced Pólya Urns

2014 ◽  
Vol 46 (02) ◽  
pp. 585-602 ◽  
Author(s):  
Li-Xin Zhang ◽  
Feifang Hu ◽  
Siu Hung Cheung ◽  
Wai Sum Chan
Keyword(s):  
Asymptotic Behavior ◽  
Rate Of Convergence ◽  
Clinical Studies ◽  
Asymptotic Properties ◽  
Important Application ◽  
Urn Models ◽  
Theoretical Justification ◽  
Treatment Allocation ◽  
Number Of Patients ◽  
Generalized Pólya Urn

The generalized Pólya urn has been extensively studied and is widely applied in many disciplines. An important application of urn models is in the development of randomized treatment allocation schemes in clinical studies. The randomly reinforced urn was recently proposed, but, although the model has some intuitively desirable properties, it lacks theoretical justification. In this paper we obtain important asymptotic properties for multicolor reinforced urn models. We derive results for the rate of convergence of the number of patients assigned to each treatment under a set of minimum required conditions and provide the distributions of the limits. Furthermore, we study the asymptotic behavior for the nonhomogeneous case.

scholarly journals Asymptotics in randomized urn models

2005 ◽  
Vol 15 (1B) ◽  
pp. 914-940 ◽  
Author(s):  
Zhi-Dong Bai ◽  
Feifang Hu
Keyword(s):  
Urn Models

Urn Models and Yao’s Formula

1999 ◽  
pp. 100-112
Author(s):  
Danièle Gardy ◽  
Laurent Némirovski
Keyword(s):  
Urn Models

Urn models and categoricity

1978 ◽  
Vol 7 (1) ◽  
Author(s):  
Philip Olin
Keyword(s):  
Urn Models
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