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Stochastic aspects of Lanchester's theory of warfare

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

J. F. C. Kingman
J. F. C. Kingman*
Affiliation:
Isaac Newton Institute, Cambridge
*
∗ Postal address: University of Cambridge, Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, UK. Email address: [email protected]
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Abstract

A Markov chain model for a battle between two opposing forces is formulated, which is a stochastic version of one studied by F. W. Lanchester. Solutions of the backward equations for the final state yield martingales and stopping identities, but a more powerful technique is a time-reversal analogue of a known method for studying urn models. A general version of a remarkable result of Williams and McIlroy (1998) is proved.

Keywords

Markov chainabsorbing statestopping timemartingales

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 60G44: Martingales with continuous parameter
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 455 - 465
Copyright
Copyright © Applied Probability Trust 2002 

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References

Chung, K. L. (1967). Markov Chains with Stationary Transition Probabilities. Springer, Berlin.Google Scholar
Cummings, N. (2001). Frederick Lanchester. OR Newsletter, November 2001, 25–27.Google Scholar
Goldie, C. M. (1977). Lanchester square-law battles: transient and terminal distributions J. Appl. Prob. 14, 604–610.Google Scholar
Kingman, J. F. C. (1999). Martingales in the OK Corral. Bull. London Math. Soc. 31, 601–606.CrossRefGoogle Scholar
Kingman, J. F. C., and Volkov, S. E. (2002). Solution of the OK Corral model via decoupling of Friedman's urn. To appear in J. Theoret. Prob.Google Scholar
Ricardo, H. (1948). Obituary of F. W. Lanchester. Obituary Notices R. Soc. 16, 757–766.Google Scholar
Williams, D., and McIlroy, P. (1998). The OK Corral and the power of the law (a curious Poisson-kernel formula for a parabolic equation). Bull. London Math. Soc. 30, 166–170.CrossRefGoogle Scholar