基于Monte Carlo方法的一对二马尔可夫随机格斗模型

One-on-Two Markov Duel Model with Monte Carlo Method

讨论了一对二马尔可夫随机格斗双方获胜概率计算问题。提出了一种新颖的一对二马尔可夫随机格斗任意对抗回合双方获胜概率的计算方法,该方法首先基于Monte Carlo仿真计算各个对抗回合中双方发射次序的概率分布,再利用全概率公式确定马尔可夫链的状态转移概率矩阵,从而克服了马尔可夫随机格斗模型往往只能提供无限对抗回合之后格斗双方获胜概率的缺点,为运用马尔可夫随机格斗研究火力运用和弹药分配提供了新途径,并用实例说明了该方法的有效性。

The wining probability computing problem with one-on-two Markov stochastic duel is discussed. A novel method is proposed for computing the wining probability of any side with one-on-two Markov stochastic duel. First,the distribution of shooting order of each round is calculated by Monte Carlo method,and the state transferring probability matrix is determined by using total probability theorem. So the shortcoming that Markov stochastic duel can only offer wining probability for infinite round is overcome. This is a new way for research on fire application and Ammunition distribution by applying Markov stochastic duel method. A numerical example is given to demonstrate its effectiveness.