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Ehrenfest urn models

Published online by Cambridge University Press:  14 July 2016

Samuel Karlin  and
James McGregor
Samuel Karlin
Affiliation:
Stanford University
James McGregor
Affiliation:
Stanford University
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Extract

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 state i if there are i balls in urn I, N − i balls 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 distribution

When an event occurs a ball is chosen at random (each of the N balls has probability 1/N to be chosen), removed from its urn, and then placed in urn I with probability p, in urn II with probability q = 1 − p, (0 < p < 1).

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 2 , December 1965 , pp. 352 - 376
Copyright
Copyright © Applied Probability Trust 

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