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Note an a death process

Published online by Cambridge University Press:  14 July 2016

S. A. De Vries ,
A. J. Stam  and
J. Reddingius
S. A. De Vries*
Affiliation:
Rijksuniversiteit Groningen
A. J. Stam*
Affiliation:
Rijksuniversiteit Groningen
J. Reddingius*
Affiliation:
Rijksuniversiteit Groningen
*
∗Postal address: Mathematisch Instituut, Rijksuniversiteit Groningen, Postbus 800, Groningen, The Netherlands.
∗Postal address: Mathematisch Instituut, Rijksuniversiteit Groningen, Postbus 800, Groningen, The Netherlands.
∗Postal address: Mathematisch Instituut, Rijksuniversiteit Groningen, Postbus 800, Groningen, The Netherlands.
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Abstract

The forward equations for the death process in ℕ2 with Q-matrix determined by q(i, j; i − 1, j) = αij, i ≧ 1, q(i, j; i, j − 1) = μj, j ≧ 1 are solved by giving a special interpretation to this Q-matrix.

Keywords

DEATH PROCESSFORWARD EQUATIONSPREDATOR-PREY MODEL
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 853 - 855
Copyright
Copyright © Applied Probability Trust 1980 

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References

Billard, L. (1977) On Lotka–Volterra predator-prey models. J. Appl. Prob. 14, 375–381.CrossRefGoogle Scholar
Billard, L., Lacayo, H. and Langberg, N. A. (1979) The symmetric m-dimensional simple epidemic process. J. R. Statist. Soc. B 41, 196–202.Google Scholar
De Vries, S. A. (1978) A stochastic model for a prey population attacked by a predator population which is subject to a death process. Report TW-197, Mathematisch Instituut, Rijksuniversiteit Groningen.Google Scholar
Nicholson, A. J. and Bailey, V. A. (1935) The balance of animal populations. Proc. Zool. Soc. Lond. II, 551–598.Google Scholar
Reddingius, J. (1975) Models and statistics in population ecology. In Proc. 8th Internat. Biometric Conference , ed. Corsten, L. C. A. and Postelnicu, T., Acad. Republ. Soc. România, Bucharest, 287–300.Google Scholar
Severo, N. C. (1969) A recursion theorem on solving differential-difference equations and application to some stochastic processes. J. Appl. Prob. 6, 673–681.Google Scholar