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The advancing wave in a spatial birth process

Published online by Cambridge University Press:  14 July 2016

H. E. Daniels
H. E. Daniels*
Affiliation:
University of Birmingham
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Abstract

It is known that, in the deterministic model of a one-dimensional spatial linear birth process, a finite initial distribution of individuals develops into an advancing wave with the minimum velocity possible for such waves. In this paper, the spatial covariance density of the process is studied in the vicinity of a point moving outwards with a given velocity. Its behaviour casts doubt on the applicability of the deterministic result to individual realisations of the process.

Keywords

SPATIAL BIRTH PROCESSADVANCING WAVESADDLEPOINT APPROXIMATIONDIFFUSION APPROXIMATIONCOVARIANCE DENSITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 689 - 701
Copyright
Copyright © Applied Probability Trust 1977 

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Footnotes

An earlier version of this paper was presented to the Sixth Conference on Stochastic Processes and their Applications, Tel Aviv, June 1976.

References

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