We show several results on convergence of the Monte Carlo method applied to consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Our method is based on combination of several new concepts. We work with the dissipative weak solutions that can be seen as a universal closure of consistent approximations. Further, we apply the set-valued version of the Strong law of large numbers for general multivalued mapping with closed range and the Koml\'os theorem on strong converge of empirical averages of integrable functions. Theoretical results are illustrated by a series of numerical simulations obtained by an unconditionally convergent viscosity finite volume method combined with the Monte Carlo method.

翻译：我们展示了将蒙特卡洛方法应用于初始数据不确定的等熵欧拉气体动力学系统的一致性逼近时的若干收敛性结果。我们的方法基于若干新概念的组合。我们采用耗散弱解作为一致性逼近的通用闭包。进一步，我们应用具有闭值域的一般多值映射的集值强大数定律，以及可积函数经验均值强收敛的Komlós定理。理论结果通过一系列数值模拟进行了验证，这些模拟采用无条件收敛的黏性有限体积方法与蒙特卡洛方法相结合的方式获得。