I am a beginner in probability theory, and have a very basic and limited understanding of the random processes, but interested in understanding them more.
In case of wide sense stationary processes, what is the benefit of "relaxing" the the strict sense stationary rule by limiting time shift invariance to only bivariate joint distributions? In other words, what is the "gain" in not requiring the time shift invariance rule with the trivariate joint distributions (or may be even the higher order multivariate joint distributions) of the elements of the random process in the wide sense stationary process definition?
thanks
The point is that in the case of normal (Gaussian) processes, i.e. all finite dimensional distributions are normal, wide sense stationary processes are also strict sense stationary. Normal processes are the most used model of stochastic processes.
Further a number of techniques (least square f.e.) depend only on the first two moments of the processes, so one can prove more general results for wide sense stationary processes without requiring strict stationarity.