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Commutative nonstationary stochastic fields. (English) Zbl 1068.60051
Summary: The paper is devoted to further development of commutative nonstationary field themes. A more complicated variant of commutative field with nonstationary rank 2, carrying into more general situation for correlation function is studied. A condition of consistency for commutative field is developed. The following semigroup structures of correlation theory for disturbances and semigroups are used in this case: \(T_t (\varepsilon ) = \exp \, (it A_{\varepsilon })\), \(A_{\varepsilon } = A_1 + \varepsilon A_2\), \(| \varepsilon | \ll 1\).
MSC:
60G12 General second-order stochastic processes
47D99 Groups and semigroups of linear operators, their generalizations and applications
47N30 Applications of operator theory in probability theory and statistics
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