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Displaying similar documents to “Distributions of sojourn time, maximum and minimum for pseudo-processes governed by higher-order heat-type equations.”

Weakly stationary processes with non–positive autocorrelations

Šárka Došlá, Jiří Anděl (2010)

Kybernetika

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We deal with real weakly stationary processes { X t , t ∈ ℤ } with non-positive autocorrelations { r k } , i. e. it is assumed that r k ≤ 0 for all k = 1 , 2 , ⋯ . We show that such processes have some special interesting properties. In particular, it is shown that each such a process can be represented as a linear process. Sufficient conditions under which the resulting process satisfies r k ≤ 0 for all k = 1 , 2 , ⋯ are provided as well.