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Multidimensional right-shift processes

Published online by Cambridge University Press:  01 July 2016

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

Let v be a positive integer and for each k = 1, · · ·, v let mk and Nk be a positive and a non-negative integer, respectively. Denote by S'Nk,mk the set of (mk + 1) -tuples rk = (rk,mk, · · ·, rk,1, rk,0) having non-negative components summing to Nk, and by Xk(t) = (Xk,mk(t), · · ·, Xk,1(t), Xk,0(t)) an (mk + 1)-tuple random variable taking on values only from the set S′Nk,mk.

Type
II. Some Particular Epidemic and Cell Models
Information
Advances in Applied Probability , Volume 3 , Issue 2 , Autumn 1971 , pp. 200 - 201
Copyright
Copyright © Applied Probability Trust 1971 

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References

Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Charles Griffin and Co. Ltd., London.Google Scholar
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Severo, N. C. (1969a) Right-shift processes, Proc. Nat. Acad. Sci. 64, 1162–1164.Google Scholar
Severo, N. C. (1969b) A recursion theorem on solving differential-difference equations and applications to some stochastic processes, J. Appl. Prob. 6, 673–681.CrossRefGoogle Scholar