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Some results for general cell-size-dependent branching processes

Published online by Cambridge University Press:  14 July 2016

Aidan Sudbury  and
Peter Clifford
Aidan Sudbury
Affiliation:
Bristol University
Peter Clifford
Affiliation:
Bristol University
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Abstract

A general model for the growth and division of cells in which the growth rate and division probability at any instant depend only on their size at that time is introduced. Conditions under which (a) the distribution of cell-size at division converges ergodically, (b) the sizes tend to 0 or ∞, are exhibited, and bounds to the correlation between the sizes at division of sister cells are given in a wide class of cases.

Keywords

BRANCHING PROCESSSIZE-DEPENDENTCELL-SIZECORRELATION BETWEEN SISTER LIFE SPANS
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 289 - 298
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Clifford, P. and Sudbury, A. W. (1971) The linear cell-size-dependent branching process. J. Appl. Prob. 9, 687–696.Google Scholar
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[3] Loève, M. (1960) Probability Theory. Van Nostrand, Princeton.Google Scholar
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[5] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. II. Chapters VI and XII. John Wiley, New York.Google Scholar