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Avtomatika i Telemekhanika, 2007, Issue 3, Pages 83–93 (Mi at954)  
Stochastic Systems

Orthogonal expansions of the nonlinear functionals of the Gaussian process and their application to statistical analysis

M. E. Shaikin

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
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Abstract: Orthogonal expansion of the space of quadratically integrable nonlinear functionals of the Gaussian random process was considered. The problem of explicit construction of the expansion terms was restated as generation of the differential equations for its coordinate functions. The method of canonical expansions from the linear statistical analysis was generalized to the nonlinear case on the basis of the results obtained.
Presented by the member of Editorial Board: B. M. Miller

Received: 20.04.2006
English version:
Automation and Remote Control, 2007, Volume 68, Issue 3, Pages 446–455
DOI: https://doi.org/10.1134/S000511790703006X
Bibliographic databases:
Document Type: Article
PACS: 02.50. Fz
Language: Russian
Citation: M. E. Shaikin, “Orthogonal expansions of the nonlinear functionals of the Gaussian process and their application to statistical analysis”, Avtomat. i Telemekh., 2007, no. 3, 83–93; Autom. Remote Control, 68:3 (2007), 446–455
Citation in format AMSBIB
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\transl
\jour Autom. Remote Control
\yr 2007
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\issue 3
\pages 446--455
\crossref{https://doi.org/10.1134/S000511790703006X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33947575730}
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