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Short Communications
On Higher Order Spectral Measures of Ergodic Stationary Processes
Ya. G. Sinai Moscow
Abstract:
In this paper some necessary conditions for the ergodicity of stationary processes belonging to the Fortet class [4] are given in terms of higher order spectral moments. These conditions lead to some new ergodic theorems for such processes and to the fact that certain spectral measures uniquely determine the corresponding processes.
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Theory of Probability and its Applications, 1963, 8:4, 429–436
Received: 26.05.1962
Citation:
Ya. G. Sinai, “On Higher Order Spectral Measures of Ergodic Stationary Processes”, Teor. Veroyatnost. i Primenen., 8:4 (1963), 463–470; Theory Probab. Appl., 8:4 (1963), 429–436
Citation in format AMSBIB
\Bibitem{Sin63}
\by Ya.~G.~Sinai
\paper On Higher Order Spectral Measures of Ergodic Stationary Processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1963
\vol 8
\issue 4
\pages 463--470
\mathnet{http://mi.mathnet.ru/tvp4693}
\transl
\jour Theory Probab. Appl.
\yr 1963
\vol 8
\issue 4
\pages 429--436
\crossref{https://doi.org/10.1137/1108048}
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http://mi.mathnet.ru/eng/tvp4693 http://mi.mathnet.ru/eng/tvp/v8/i4/p463
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