On Multi-Dimensional Stationary Random Processes

The necessary and sufficient conditions for the regularity as well as for "the maximum regularity" of $n$-dimensional stationary random processes $(x_1 (t),x_2 (t), \cdots ,x_n (t))$ with continuous time are obtained. Wold's development "for the process" is also proved.

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Bibliographic Details
Published inTheory of probability and its applications Vol. 3; no. 4; pp. 425 - 428
Main Author Gladyshev, E. G.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.10.1958
Subjects
Hilbert space
Markov analysis
Random variables
Stochastic models
Theorems
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Summary:The necessary and sufficient conditions for the regularity as well as for "the maximum regularity" of $n$-dimensional stationary random processes $(x_1 (t),x_2 (t), \cdots ,x_n (t))$ with continuous time are obtained. Wold's development "for the process" is also proved.
ISSN:0040-585X
1095-7219
DOI:10.1137/1103035