scholarly journals Nonlinear randomized urn models: a stochastic approximation viewpoint

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Sophie Laruelle ◽  
Gilles Pagès
Keyword(s):  
Stochastic Approximation ◽  
Urn Models

scholarly journals Randomized urn models revisited using stochastic approximation

2013 ◽  
Vol 23 (4) ◽  
pp. 1409-1436 ◽  
Author(s):  
Sophie Laruelle ◽  
Gilles Pagès
Keyword(s):  
Stochastic Approximation ◽  
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).

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