The Distribution of the Hit Times and the Kill Probability in a Stochastic Duel with Searching

The paper studies the model of a stochastic duel with searching by using conditional stochastic processes and selects the probability distribution of the hit times and the kill probability in the time 0, tas indexes to evaluate shot effects. Two suppositions are adopted to the distributions of the random variables of shot time intervals-an exponential distribution and an arbitrary distribution. The results deduced in the condition of the exponential distribution are satisfactory and for the secondary assumption, the paper puts forward the formula to calculate the distribution of hit times.