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Some aspects of the non-asymptotic behaviour of a two-dimensional invasion process

Published online by Cambridge University Press:  14 July 2016

D. Y. Downham  and
S. B. Fotopoulos
D. Y. Downham*
Affiliation:
University of Liverpool
S. B. Fotopoulos*
Affiliation:
University of Liverpool
*
∗ Postal address: Department of Computational and Statistical Science, University of Liverpool, Victoria Building, Brownlow Hill, P.O. Box 147, Liverpool L69 3BX, U.K.
∗ Postal address: Department of Computational and Statistical Science, University of Liverpool, Victoria Building, Brownlow Hill, P.O. Box 147, Liverpool L69 3BX, U.K.
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Abstract

Normal and abnormal cells are positioned at the vertices of a regular two-dimensional lattice. Abnormal cells divide k times as fast as normal cells. Whenever a cell divides, the daughter is the same type as the parent and replaces an adjacent cell. The Kolmogorov forwards and backwards equations are derived, and then used to obtain bounds for the distribution function of the time when all the abnormal cells are forced from the plane. These bounds are used to comment on the non-asymptotic variance of the number of abnormal cells at a given time and on a method of estimating k.

Keywords

SPATIAL PROCESSINVASIONTUMOR GROWTHKOLMOGOROV EQUATIONS

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 732 - 737
Copyright
Copyright © Applied Probability Trust 

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References

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