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Lanchester square-law battles: Transient and terminal distributions

Published online by Cambridge University Press:  14 July 2016

Charles M. Goldie
Charles M. Goldie*
Affiliation:
University of Sussex
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Abstract

For a battle governed by the stochastic version of Lanchester's square law the transient distribution of state is found; also various terminal distributions. The terminal distributions arise also in certain related random walks.

Keywords

BATTLESCONFLICTSLANCHESTER SQUARE-LAWMARKOV CHAINSTRANSIENT DISTRIBUTIONTERMINAL DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 604 - 610
Copyright
Copyright © Applied Probability Trust 1977 

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References

Bowen, K. C. (1973) Mathematical battles. Bull. Inst. Math. Appl. 9, 310–315.Google Scholar
Brown, R. H. (1963) Theory of combat: the probability of winning. Opns. Res. 11, 418–425.CrossRefGoogle Scholar
Gye, R. and Lewis, T. (1974) Some new results relating to Lanchester's square law. Research Report, Dept. of Math. Statistics and Sub-Dept. of O. R., University of Hull.Google Scholar
Gye, R. and Lewis, T. (1976) Lanchester's equations: mathematics and the art of war. Math. Scientist 1, 107–119.Google Scholar