Stochastic conditional and unconditional warfare

This article constructs a foundation for warfare at the individual level, where agents in two groups fire and absorb shots according to a non-stationary Poisson process. We determine for generalized forms of warfare the conditional and unconditional point probabilities of a certain number of agents in each group through time, and the conditional and unconditional expected sizes and variances. Conditional variables are especially useful in modern warfare since these allow for updated intelligence. We determine the conditions for discrepancies between the stochastic version and the associated Lanchester model. Correspondence is demonstrated for square warfare for large groups where the probability that a group goes extinct is negligible. For linear warfare equivalence occurs for the conditional case, whereas for the unconditional case correspondence arises at the limit where the covariance of the group sizes approaches zero. Finally the stochastic model is tested against newly released empirics for the Ardennes Campaign during World War II.