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A note on the Ehrenfest multiurn model

Published online by Cambridge University Press:  14 July 2016

Norman C. Severo
Norman C. Severo*
Affiliation:
State University of New York at Buffalo
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Extract

Denote by SN,r the set of r-tuples n having non-negative integer components summing to N, and by ei the r-tuple having a one in the ith position and zeros elsewhere. For m and n belonging to SN r, we let P(n, t|m, s) represent the transition probability of moving from state m at time s to state n at time t. Bartlett's conservative process [1] assumes that for n–ei + ej and n ∈ SN,r and Δt > 0 where the λij(t) are non-negative continuous functions of t.

Type
Short Communications
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 444 - 445
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B 11, 211–229.Google Scholar
[2] Jensen, A. (1948) An elucidation of A. K. Erlang's statistical works through the theory of stochastic processes. The Life and Works of A. K. Erlang, by Brockmeyer, E., Halstr⊘m, H. L. & Jensen, Arne. The Copenhagen Telephone Company, Copenhagen, 23–100.Google Scholar
[3] Karlin, S. and Mcgregor, J. (1965) Ehrenfest urn models. J. Appl. Prob. 2, 352–376.CrossRefGoogle Scholar
[4] Radcliffe, J. and Staff, P. J. (1969) First-order conservative processes with multiple latent roots. J. Appl. Prob. 6, 186–194.CrossRefGoogle Scholar
[5] Srivastava, R. C. (1967) Some aspects of the stochastic model for the attachment of phages to bacteria. J. Appl. Prob. 4, 9–18.CrossRefGoogle Scholar