随机过程一阶概率分布函数的遍历性

On the Ergodicity of 1-order Probability Distribution Function of Stochastic Process

提出了随机过程一阶概率分布函数具有遍历性的一个充分必要条件(定理1和推论1),并在较弱条件下,对一般的关于随机变量函数分布定理作了进一步的推广(定理2)。利用这些结果,讨论了随机初相位周期过程一阶分布函数的遍历性(推论2)。最后,作为应用,用具有一维均匀分布的随机过程构造了一种白噪音模型。

A necessary and sufficient condition with ergodic of 1-order probability distribution function of stochastic process (Theorem 1 and Corollary 1) and extended the general distribution theorem of stochastic variable under the case of weakly condition (theorem2) are presented.Based on these results, the ergotic of 1-order distribution function of stochastic primary phase periodic process are derived (Corollary 2). And at the last, a model of white noise are constructed via the stochastic process with 1-dimensional evenly distributed stochastic process.