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Teoriya Veroyatnostei i ee Primeneniya, 1964, Volume 9, Issue 2, Pages 390–394 (Mi tvp388)  

This article is cited in 80 scientific papers (total in 81 papers)

Short Communications

Some Characteristic Properties of Stochastic Gaussian Processes

A. M. Veršik

Leningrad
Abstract: In the paper spherically invariant processes are defined. The characteristic function of these processes $(\xi(t))$ in accordance with Shonberg's theorem [1] is of the form
$$ \chi(\eta)\equiv{\mathbf M}e^{i\eta}=f({\mathbf D}\eta)=\int_0^\infty e^{-\gamma{\mathbf D}\eta}\,G(d\gamma), $$
$\eta=\int\xi(t)\eta(t)\,dt$, where $G$ is some measure on $[0,\infty)$. Only if the process is spherically invariant, then 1) every extrapolation problem has a linear solution, 2) every functional transformation leaving the correlation function of the process invariant retains its measure in the space of realizations.If a spherically invariant process is stationary and ergodic, then it is Gaussian.
Received: 21.10.1963
English version:
Theory of Probability and its Applications, 1964, Volume 9, Issue 2, Pages 353–356
DOI: https://doi.org/10.1137/1109053
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. M. Veršik, “Some Characteristic Properties of Stochastic Gaussian Processes”, Teor. Veroyatnost. i Primenen., 9:2 (1964), 390–394; Theory Probab. Appl., 9:2 (1964), 353–356
Citation in format AMSBIB
\Bibitem{Ver64}
\by A.~M.~Ver{\v s}ik
\paper Some Characteristic Properties of Stochastic Gaussian Processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1964
\vol 9
\issue 2
\pages 390--394
\mathnet{http://mi.mathnet.ru/tvp388}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=165577}
\zmath{https://zbmath.org/?q=an:0141.15203}
\transl
\jour Theory Probab. Appl.
\yr 1964
\vol 9
\issue 2
\pages 353--356
\crossref{https://doi.org/10.1137/1109053}
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  • This publication is cited in the following 81 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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