Study on Winning Probabilities ofTwo-versus-Two Stochastic Duel with Searching

摘要

The stochastic duel theory comes from applying stochastic process to Lanchester equa-tion. The stochastic duel with searching is a kind of duel, not less than one of whose two contestantsare stealthily. When on the assumption that the time intervals of two contestants is the same neg-ative exponential distribution(NED), the stochastic duel is a Markov process which is continuousin time and discrete in states. The winning probability formulas of two-versus-two stochastic duelwith searching are deduced using state transfer figure and the property of Laplace transformation.Finally the simulations and calculations are done in a true combat environment. The results of thewinning probabilities formulas are exact probabilistic solutions, which can be used to quantifica-tionally evaluate operation efficiency of more realistic small-to-moderate-size firefight models.