n个平稳随机过程之和为平稳过程的一个充分条件及其应用

A sufficient condition of sum of n stationary stochastic processes is stationary and its application

构造出两个平稳过程不平稳相依及平稳过程之和不平稳的例子.给出n个平稳随机过程之和为平稳过程的一个充分条件:设W(t)是n个平稳随机过程Xi(t)(i=1,2,...,n)之和,如果Xi(t)是两两平稳相依的,那么W(t)也是平稳随机过程.并作应用,得出一个重要结论,即X(t)平稳随机过程与其所有各阶导数(若存在的话)之和为平稳过程.

Examples that two stationary stochastic processes are not stationarily dependent and sum of stationary stochastic processes is not stationary are constructed.A sufficient condition that sum of n stationary stochastic processes is stationary is given: suppose that W(t) is sum of n stationary stochastic processes Xi(t)(i = 1,2,...,n),then W(t) is stationary stochastic process if Xi(t) is pairwise stationarily dependent.One application is given and an important conclusion that sum of stationary stochastic process X(t) and its derivatives of all orders(if exist) is stationary stochastic process,is obtained.