Lanchester’s Stochastic Model of Combat Operations

The mathematical model of the interaction of two opposing sides is considered in the form of a system of differential equations (Lanchester), the coefficients of which are random processes given by the characteristic functional. The problem is to find the first moment functions of the solution. This problem is reduced to a deterministic system of differential equations with ordinary and variational derivatives. Explicit formulas are obtained for the first two moment functions of the solution of the stochastic system. Problems with Gaussian and uniformly distributed random coefficients are considered. Numerical calculations and graphs of the behavior of the mathematical expectation and dispersion function are presented.