Approximation Techniques and Optimal Decision Making for Stochastic Lanchester Models.

摘要

This thesis extends the analysis of stochastic Lanchester models beyond the stage of mere modeling. To this end, a frame-work of statistical decision theory is superimposed on a simplified combat situation. The commander must make decisions about the amount of force he will commit to a combat in reference to a suitable cost and reward structure. Problems of both the one-stage and the multi-stage variety are studied. The one-stage decision problem requires knowledge of the probability of victory and the expected number of survivors. A complete solution to this problem is given, based on the use of a martingale central limit theorem. The multi-stage decision problem requires the distribution of the force level configuration as a function of time. These distributions are approximated through the use of diffusion approximations. A two-stage problem is solved using these approximations and backward induction.