The method of distributions is developed for systems that are governed by hyperbolic conservation laws with stochastic forcing. The method yields a deterministic equation for the cumulative density distribution (CDF) of a system state, e.g., for flow velocity governed by an inviscid Burgers' equation with random source coefficients. This is achieved without recourse to any closure approximation. The CDF model is verified against MC simulations using spectral numerical approximations. It is shown that the CDF model accurately predicts the mean and standard deviation for Gaussian, normal and beta distributions of the random coefficients.

中文翻译：

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具有随机强迫的系统的分布方法

分布方法是为受具有随机强迫的双曲线守恒定律支配的系统开发的。该方法产生系统状态的累积密度分布（CDF）的确定性方程，例如，由具有随机源系数的无粘性伯格斯方程控制的流速。这是在不求助于任何闭包近似的情况下实现的。CDF 模型通过使用谱数值近似的 MC 模拟进行验证。结果表明，CDF 模型准确地预测了随机系数的高斯分布、正态分布和 beta 分布的均值和标准差。