论文标题
一种用于模拟非高斯和非平稳随机过程的新数值方案
A new numerical scheme for simulating non-gaussian and non-stationary stochastic processes
论文作者
论文摘要
本文提出了一种新的数值方案，用于模拟由其边际分布函数和协方差函数指定的随机过程。首先生成随机样品以自动满足目标边缘分布函数。提出了一种迭代算法，以将随机样品的模拟协方差函数与目标协方差函数匹配，并且只有几次迭代可以收敛到所需的精度。基于Karhunen-Loève扩展和多项式混乱扩展的几种显式表示，进一步开发了以串联形式所获得的随机样品。建议的方法可以应用于非高斯和非平稳随机过程，三个例子说明了它们的准确性和效率。
This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal distribution functions. An iterative algorithm is proposed to match the simulated covariance function of stochastic samples to the target covariance function, and only a few times iterations can converge to a required accuracy. Several explicit representations, based on Karhunen-Loève expansion and Polynomial Chaos expansion, are further developed to represent the obtained stochastic samples in series forms. Proposed methods can be applied to non-gaussian and non-stationary stochastic processes, and three examples illustrate their accuracies and efficiencies.
