On a stochastic version of Lanchester's model of combat

TL;DR

This paper revisits a stochastic, discrete-time version of Lanchester's combat model, providing simplified derivations and exact solutions to address the model's limitations due to random fluctuations.

Contribution

It introduces a refined, exact solution approach for a stochastic Lanchester model, improving upon previous scattered results and simplifying the analysis.

Findings

Exact solutions for the stochastic model are derived.

Simplified derivations enhance understanding of the model.

Refinements improve the model's applicability to real combat scenarios.

Abstract

Lanchester's model of combat has certain deficiencies in its standard form arising from the neglect of the influence of random fluctuations. Several approaches to rectify this have been proposed and various results are scattered throughout the literature. Here, a discrete-time stochastic version, which is amenable to exact solution, is revisited with the aim of deriving key results within one setting. The exposition simplifies and provides refinements to earlier derivations and analysis.