Journal of Applied Probability

Stochastic aspects of Lanchester's theory of warfare

J. F. C. Kingman

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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.

Article information

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

Dates
First available: 8 October 2002

Permanent link to this document
http://projecteuclid.org/euclid.jap/1034082119

Digital Object Identifier
doi:10.1239/jap/1034082119

Mathematical Reviews number (MathSciNet)
MR1928882

Zentralblatt MATH identifier
1028.60041

Subjects
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

Keywords
Markov chain absorbing state stopping time martingales

Citation

Kingman, J. F. C. Stochastic aspects of Lanchester's theory of warfare. Journal of Applied Probability 39 (2002), no. 3, 455--465. doi:10.1239/jap/1034082119. http://projecteuclid.org/euclid.jap/1034082119.


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