平稳随机过程模拟的一个快速Hartley变换方法

由平稳随机过程谱表示定理导出了平稳随机过程蒙特卡罗模拟的一个快速Hartley变换方法。按照该方法，样本过程可直接由一正弦和余弦函数和的级数公式计算产生。可以证明，当级数项数N足够大时，模拟的样本过程可准确地反映平稳随机过程规定的性质；当样本过程足够多时，其总体均值和总体自相关函数均趋于相应目标函数。方法有如下一些特点：模拟的样本过程由相互正交的两个过程迭加而成，样本过程具备各态历经性质，样本过程随着级数项数N趋于无穷而渐近呈正态分布，可直接利用快速Hartley变换来大大提高模拟的计算效率。

Simulation of Stationary Stochastic Processes by Fast Hartley Transform

Based on the spectral representation theorem of stationary stochastic processes, in this paper, a method is propesed for Monte Carlo simulation of stationary stochastic processes by the fast Hartley transform. Following this method, sample processes can be generated using a cosine and sine series formula. These sample processes accurately reflect the prescribed probabilistic characteristics of the stationary stochastic process when the number of the terms in the series is large. The ensemble-averaged expected value and autocorrelation function approach the corresponding target functions as the sample size increases. The method also has the following advantages: the sample processes are composed of two mutually orthogonal processes, the sample processes are ergodic, the sample processes are asymptotically Gaussian as the number of the terms in the series tends to be infinite, the sample processes can be generated directly by the fast Hartley transform with great computational efficiency.