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

摘要

The stochastic duel theory comes from applying stochastic process to Lancbester equation. The stochastic duel with searching is a kind of duel, not less than one of whose two contestants are stealthily. When on the assumption that the time intervals of two contestants is the same negative exponential distribution(NED), the stochastic duel is a Markov process which is continuous in time and discrete in states. 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 simulations and calculations are done in a true combat environment. The results of the winning probabilities formulas are exact probabilistic solutions, which can be used to quantificationally evaluate operation efficiency of more realistic small-to-moderate-size firefight models.