stationary process

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A stochastic process is said to be stationary (or strictly stationary) if the joint distribution of the sequence of measurements x1+l, x2+l,…, xk+l is, for all k, independent of l. A less restrictive requirement is that the expected value of the x-values should be constant and that, for all k, the covariance between the values of xk and xk+l should depend only on the lag l—such a process is described as weakly stationary (or second-order stationary). See also Markov process.

Subjects: Probability and Statistics.

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