联合平稳随机过程导数的联合平稳性

On Joinly Stationarities of their Derivatives of Joinly Stationary Random Processes

目的为了讨论联合平稳随机过程{X(t),t∈T}和{Y(t),t∈T}的导数{X(k)(t),t∈T}与{Y(l)(t),t∈T}(0≤k,l≤n)的联合平稳性.方法利用了平稳随机过程和联合平稳性的定义及数学归纳法.结果分别证明了{X(t),t∈T})和{Y(′t),t∈T}、{X(′t),t∈T}和{Y(t),t∈T}的联合平稳性,在此基础上给出了它们的两个推论.结论证明了随机过程与{X(k)(t)±Y(l)(t),t∈T,0≤k,l≤n)}的联合平稳性,得到了三个重要结论,为讨论联合平稳随机过程导数的其它相关性质提供了方便.

Aim Tto discuss joinly stationarity of their derivatives {X（k）（t）,t∈T} and {Y（1）（t）,t∈T}（0≤k,l≤n）of joinly stationary stochastic processes {X（t）,t∈T}and {Y（t）,t∈T}.Methods The definition of stationary random processes and joinly stationarity and ,the method of mathematics induction are used.Results The joinly stationarities of{X（t）,t∈T}and{Y′（t）,t∈T},{X′（t）,t∈T} and {Y（t）,t∈T}are proved respectively, and then their two deductions are obtained Conclusion Joinly stationarity of their derivatives {X（k）（t）,t∈T}and Y（l）（t）,t∈T}（0≤k,l≤n）are proved, and thenthree important conclusions are drawn, which can serve for the discussion of other relative properties.