Stationary sequence - Alchetron, The Free Social Encyclopedia

In probability theory – specifically in the theory of stochastic processes, a stationary sequence is a random sequence whose joint probability distribution is invariant over time. If a random sequence X_j is stationary then the following holds:

F X n , X n + 1 , … , X n + N − 1 ( x n , x n + 1 , … , x n + N − 1 ) = F X n + k , X n + k + 1 , … , X n + k + N − 1 ( x n , x n + 1 , … , x n + N − 1 ) ,

where F is the joint cumulative distribution function of the random variables in the subscript.

If a sequence is stationary then it is wide-sense stationary.

If a sequence is stationary then it has a constant mean (which may not be finite):

E ( X [ n ] ) = μ for all n .

References

Stationary sequence Wikipedia

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