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A notion of a wide-sense Markov process of order k ≥ 1, , is introduced as a direct generalization of Doob’s notion of wide-sense Markov process (of order k=1 in our terminology). A base for investigation of the covariance structure of is the k-dimensional process . The covariance structure of is considered in the general case and in the periodic case. In the general case it is shown that iff is a k-dimensional WM(1) process and iff the covariance function of has the triangular property....
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