Journal of Applied Probability

Stochastic aspects of Lanchester's theory of warfare

J. F. C. Kingman

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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.

Article information

J. Appl. Probab. Volume 39, Number 3 (2002), 455-465.

First available in Project Euclid: 8 October 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
Secondary: 60G44: Martingales with continuous parameter

Markov chain absorbing state stopping time martingales


Kingman, J. F. C. Stochastic aspects of Lanchester's theory of warfare. J. Appl. Probab. 39 (2002), no. 3, 455--465. doi:10.1239/jap/1034082119.

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