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The principle of the diffusion of arbitrary constants

Published online by Cambridge University Press:  14 July 2016

Andrew D. Barbour
Andrew D. Barbour*
Affiliation:
University of Cambridge
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Abstract

Equations are derived describing a central limit type large population approximation for continuous time Markov lattice processes in one or more dimensions, such as are commonly encountered in biological models. A method of solving the equations using only the deterministic solution of the process is explained, and it is extended by the use of a martingale argument to provide more detailed information about the process.

Keywords

MARKOV POPULATION PROCESSESEPIDEMICRUMOURMARTINGALECOMPETITION PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 3 , June 1972 , pp. 519 - 541
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Bailey, N. T. J. (1964) The Elements of Stochastic Processes. (Chapter 10). John Wiley, New York.Google Scholar
[2] Bailey, N. T. J. (1968) A perturbation approximation to the simple stochastic epidemic in a large population. Biometrika 55, 199.Google Scholar
[3] Daley, D. J. and Kendall, D. G. (1965) Stochastic rumours. J. Inst. Math. Appl. 1, 42–55.Google Scholar
[4] Whittle, P. (1957) On the use of the normal approximation in the treatment of stochastic processes. J. Roy. Statist. Soc. Ser. B. 19, 268.Google Scholar