| 一类搜索型随机格斗的获胜概率研究 |
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| 引用本文： | 聂凯,刘忠,薛锋.一类搜索型随机格斗的获胜概率研究[J].数学的实践与认识,2009,39(18). |
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| 作者姓名： | 聂凯 刘忠 薛锋 |
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| 作者单位： | 海军工程大学,电子工程学院,湖北,武汉,430033 |
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| 摘 要： | 把随机过程分析引入Lanchester方程就形成了随机格斗理论.运用随机格斗理论研究了潜艇协同隐蔽攻击水面舰艇编队获胜概率的数学模型,利用状态转移图和Laplace变换的性质推导出了2对2搜索型随机格斗中双方的获胜概率公式,并结合潜艇协同隐蔽攻击水面舰艇的实际,计算分析了格斗双方的获胜概率.利用这一公式可以得到概率上的精确解,能够被用来定量评估潜艇协同隐蔽攻击水面舰艇编队的作战效能.
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| 关 键 词： | 搜索型随机格斗 马尔可夫过程 获胜概率 状态转移图 |
The Winning Probabilities of a Kind of Stochastic Duel with Searching |
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| NIE Kai,LIU Zhong,XUE Feng.The Winning Probabilities of a Kind of Stochastic Duel with Searching[J].Mathematics in Practice and Theory,2009,39(18). |
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| Authors: | NIE Kai LIU Zhong XUE Feng |
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| Abstract: | The stochastic duel theory comes from applying stochastic process to Lanchester equation. The mathematics models of submarine's coordinated stealthily attacking surface warship formation are given according to stochastic duel theory and the winning probability formulas of two-versus-two stochastic duel with searching are deduced using state transfer figure and the property of Laplace transformation. Finally the winning probabilities of submarine's coordinated stealthily attacking surface vessel are gotten in the true combat environment. The results of the winning probabilities formulas are exact probabilistic solutions, which can be used to quantifacationally evaluate operation efficiency of submarine's coordinated stealthily attacking surface warship formation. |
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| Keywords: | stochastic duel with searching Markov process winning probability state transfer figure |
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