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Due to the increasing use of autonomous aerial vehicles in military applications such as search, surveillance and reconnaissance of mobile targets, the study of (multi-player) pursuit-evasion (PE) differential game has revived. As a basis for studying multi-player games, we focus on a two-player stochastic PE game. Based on the classical differential game theory, we derive the analytical value function for a two-player stochastic PE game using the Dubin's car model. Moreover, we address the issue of the finite expectation of the capture time in both the perfect and the imperfect state information cases. Sufficient conditions are provided in terms of the players' speeds, measurement accuracy and the capture range of the pursuer. These results can provide insight for stochastic PE game problems and are useful for solving multi-player games.