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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: director@newton.cam.ac.uk
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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

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